LMFDB - Embedded newform 507.2.k.k.488.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			488.8
Character	$\chi$	$=$	507.488
Dual form			507.2.k.k.80.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.339800 - 1.26815i) q^{2} +(1.60126 - 0.660289i) q^{3} +(0.239309 - 0.138165i) q^{4} +(-2.12536 + 2.12536i) q^{5} +(-1.38145 - 1.80627i) q^{6} +(2.82123 + 0.755945i) q^{7} +(-2.11323 - 2.11323i) q^{8} +(2.12804 - 2.11458i) q^{9} +O(q^{10})$	\(q+(-0.339800 - 1.26815i) q^{2} +(1.60126 - 0.660289i) q^{3} +(0.239309 - 0.138165i) q^{4} +(-2.12536 + 2.12536i) q^{5} +(-1.38145 - 1.80627i) q^{6} +(2.82123 + 0.755945i) q^{7} +(-2.11323 - 2.11323i) q^{8} +(2.12804 - 2.11458i) q^{9} +(3.41747 + 1.97308i) q^{10} +(2.57352 - 0.689573i) q^{11} +(0.291966 - 0.379251i) q^{12} -3.83461i q^{14} +(-1.99989 + 4.80659i) q^{15} +(-1.68549 + 2.91935i) q^{16} +(-0.0994162 - 0.172194i) q^{17} +(-3.40472 - 1.98013i) q^{18} +(1.37337 - 5.12548i) q^{19} +(-0.214967 + 0.802269i) q^{20} +(5.01665 - 0.652364i) q^{21} +(-1.74897 - 3.02930i) q^{22} +(1.65038 - 2.85855i) q^{23} +(-4.77917 - 1.98848i) q^{24} -4.03430i q^{25} +(2.01129 - 4.79111i) q^{27} +(0.779591 - 0.208891i) q^{28} +(3.23258 + 1.86633i) q^{29} +(6.77505 + 0.902881i) q^{30} +(-0.550550 - 0.550550i) q^{31} +(-1.49855 - 0.401535i) q^{32} +(3.66555 - 2.80345i) q^{33} +(-0.184586 + 0.184586i) q^{34} +(-7.60277 + 4.38946i) q^{35} +(0.217097 - 0.800060i) q^{36} +(1.32066 + 4.92878i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(0.986066 + 3.68005i) q^{41} +(-2.53195 - 6.14019i) q^{42} +(-10.0942 + 5.82790i) q^{43} +(0.520592 - 0.520592i) q^{44} +(-0.0285911 + 9.01709i) q^{45} +(-4.18587 - 1.12160i) q^{46} +(-4.29586 - 4.29586i) q^{47} +(-0.771281 + 5.78754i) q^{48} +(1.32568 + 0.765385i) q^{49} +(-5.11610 + 1.37086i) q^{50} +(-0.272889 - 0.210083i) q^{51} +13.6276i q^{53} +(-6.75928 - 0.922602i) q^{54} +(-4.00407 + 6.93525i) q^{55} +(-4.36442 - 7.55939i) q^{56} +(-1.18519 - 9.11402i) q^{57} +(1.26836 - 4.73357i) q^{58} +(0.864088 - 3.22482i) q^{59} +(0.185512 + 1.42658i) q^{60} +(1.35047 + 2.33909i) q^{61} +(-0.511103 + 0.885257i) q^{62} +(7.60218 - 4.35704i) q^{63} +8.77879i q^{64} +(-4.80075 - 3.69585i) q^{66} +(7.28944 - 1.95320i) q^{67} +(-0.0475824 - 0.0274717i) q^{68} +(0.755216 - 5.66699i) q^{69} +(8.14992 + 8.14992i) q^{70} +(-5.16536 - 1.38405i) q^{71} +(-8.96564 - 0.0284280i) q^{72} +(-3.46215 + 3.46215i) q^{73} +(5.80168 - 3.34960i) q^{74} +(-2.66381 - 6.45995i) q^{75} +(-0.379503 - 1.41633i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(-2.62241 - 9.78695i) q^{80} +(0.0570734 - 8.99982i) q^{81} +(4.33179 - 2.50096i) q^{82} +(1.84014 - 1.84014i) q^{83} +(1.11040 - 0.849243i) q^{84} +(0.577269 + 0.154679i) q^{85} +(10.8207 + 10.8207i) q^{86} +(6.40850 + 0.854033i) q^{87} +(-6.89568 - 3.98122i) q^{88} +(-1.06120 + 0.284349i) q^{89} +(11.4447 - 3.02775i) q^{90} -0.912102i q^{92} +(-1.24509 - 0.518049i) q^{93} +(-3.98807 + 6.90753i) q^{94} +(7.97458 + 13.8124i) q^{95} +(-2.66469 + 0.346516i) q^{96} +(-3.14829 + 11.7496i) q^{97} +(0.520155 - 1.94125i) q^{98} +(4.01839 - 6.90936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9}+O(q^{10}) $ 96 * q + 24 * q^9	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.339800	−	1.26815i	−0.240275	−	0.896718i	−0.975700	−	0.219112i	$-0.929684\pi$
$2$	−0.339800	−	1.26815i	−0.240275	−	0.896718i	0.735425	−	0.677606i	$-0.236983\pi$
$3$	1.60126	−	0.660289i	0.924485	−	0.381218i
$3$	1.60126	−	0.660289i	0.924485	−	0.381218i
$4$	0.239309	−	0.138165i	0.119655	−	0.0690826i
$5$	−2.12536	+	2.12536i	−0.950489	+	0.950489i	−0.998831	−	0.0483414i	$-0.984606\pi$
$5$	−2.12536	+	2.12536i	−0.950489	+	0.950489i	0.0483414	+	0.998831i	$0.484606\pi$
$6$	−1.38145	−	1.80627i	−0.563976	−	0.737405i
$7$	2.82123	+	0.755945i	1.06632	+	0.285720i	0.748982	−	0.662591i	$-0.230543\pi$
$7$	2.82123	+	0.755945i	1.06632	+	0.285720i	0.317342	+	0.948311i	$0.397210\pi$
$8$	−2.11323	−	2.11323i	−0.747141	−	0.747141i
$9$	2.12804	−	2.11458i	0.709345	−	0.704861i
$10$	3.41747	+	1.97308i	1.08070	+	0.623942i
$11$	2.57352	−	0.689573i	0.775946	−	0.207914i	0.150949	−	0.988541i	$-0.451767\pi$
$11$	2.57352	−	0.689573i	0.775946	−	0.207914i	0.624997	+	0.780627i	$0.285100\pi$
$12$	0.291966	−	0.379251i	0.0842833	−	0.109480i
$13$		0			0
$13$		0			0
$14$		−	3.83461i		−	1.02484i
$15$	−1.99989	+	4.80659i	−0.516369	+	1.24106i
$16$	−1.68549	+	2.91935i	−0.421373	+	0.729839i
$17$	−0.0994162	−	0.172194i	−0.0241120	−	0.0417632i	0.853718	−	0.520736i	$-0.174342\pi$
$17$	−0.0994162	−	0.172194i	−0.0241120	−	0.0417632i	−0.877830	+	0.478973i	$0.841009\pi$
$18$	−3.40472	−	1.98013i	−0.802499	−	0.466722i
$19$	1.37337	−	5.12548i	0.315072	−	1.17586i	−0.608850	−	0.793285i	$-0.708369\pi$
$19$	1.37337	−	5.12548i	0.315072	−	1.17586i	0.923922	−	0.382580i	$-0.124964\pi$
$20$	−0.214967	+	0.802269i	−0.0480681	+	0.179393i
$21$	5.01665	−	0.652364i	1.09472	−	0.142358i
$22$	−1.74897	−	3.02930i	−0.372881	−	0.645848i
$23$	1.65038	−	2.85855i	0.344129	−	0.596048i	−0.641066	−	0.767485i	$-0.721508\pi$
$23$	1.65038	−	2.85855i	0.344129	−	0.596048i	0.985195	+	0.171437i	$0.0548410\pi$
$24$	−4.77917	−	1.98848i	−0.975544	−	0.405897i
$25$		−	4.03430i		−	0.806861i
$26$		0			0
$27$	2.01129	−	4.79111i	0.387073	−	0.922049i
$28$	0.779591	−	0.208891i	0.147329	−	0.0394766i
$29$	3.23258	+	1.86633i	0.600274	+	0.346568i	0.769149	−	0.639069i	$-0.220680\pi$
$29$	3.23258	+	1.86633i	0.600274	+	0.346568i	−0.168875	+	0.985637i	$0.554013\pi$
$30$	6.77505	+	0.902881i	1.23695	+	0.164843i
$31$	−0.550550	−	0.550550i	−0.0988817	−	0.0988817i	0.655935	−	0.754817i	$-0.272274\pi$
$31$	−0.550550	−	0.550550i	−0.0988817	−	0.0988817i	−0.754817	+	0.655935i	$0.772274\pi$
$32$	−1.49855	−	0.401535i	−0.264908	−	0.0709820i
$33$	3.66555	−	2.80345i	0.638090	−	0.488018i
$34$	−0.184586	+	0.184586i	−0.0316563	+	0.0316563i
$35$	−7.60277	+	4.38946i	−1.28510	+	0.741955i
$36$	0.217097	−	0.800060i	0.0361828	−	0.133343i
$37$	1.32066	+	4.92878i	0.217116	+	0.810287i	0.985411	+	0.170191i	$0.0544386\pi$
$37$	1.32066	+	4.92878i	0.217116	+	0.810287i	−0.768295	+	0.640096i	$0.778895\pi$
$38$	−6.96655			−1.13012
$39$		0			0
$40$	8.98276			1.42030
$41$	0.986066	+	3.68005i	0.153998	+	0.574727i	0.999189	+	0.0402633i	$0.0128197\pi$
$41$	0.986066	+	3.68005i	0.153998	+	0.574727i	−0.845192	+	0.534464i	$0.820514\pi$
$42$	−2.53195	−	6.14019i	−0.390689	−	0.947451i
$43$	−10.0942	+	5.82790i	−1.53936	+	0.888747i	−0.540479	+	0.841358i	$0.681757\pi$
$43$	−10.0942	+	5.82790i	−1.53936	+	0.888747i	−0.998876	+	0.0473894i	$0.984910\pi$
$44$	0.520592	−	0.520592i	0.0784823	−	0.0784823i
$45$	−0.0285911	+	9.01709i	−0.00426212	+	1.34419i
$46$	−4.18587	−	1.12160i	−0.617173	−	0.165371i
$47$	−4.29586	−	4.29586i	−0.626616	−	0.626616i	0.320599	−	0.947215i	$-0.396116\pi$
$47$	−4.29586	−	4.29586i	−0.626616	−	0.626616i	−0.947215	+	0.320599i	$0.896116\pi$
$48$	−0.771281	+	5.78754i	−0.111325	+	0.835360i
$49$	1.32568	+	0.765385i	0.189384	+	0.109341i
$50$	−5.11610	+	1.37086i	−0.723526	+	0.193868i
$51$	−0.272889	−	0.210083i	−0.0382120	−	0.0294175i
$52$		0			0
$53$			13.6276i			1.87189i	0.352142	+	0.935947i	$0.385454\pi$
$53$			13.6276i			1.87189i	−0.352142	+	0.935947i	$0.614546\pi$
$54$	−6.75928	−	0.922602i	−0.919822	−	0.125550i
$55$	−4.00407	+	6.93525i	−0.539908	+	0.935149i
$56$	−4.36442	−	7.55939i	−0.583220	−	1.01017i
$57$	−1.18519	−	9.11402i	−0.156982	−	1.20718i
$58$	1.26836	−	4.73357i	0.166543	−	0.621548i
$59$	0.864088	−	3.22482i	0.112495	−	0.419836i	−0.886593	−	0.462551i	$-0.846934\pi$
$59$	0.864088	−	3.22482i	0.112495	−	0.419836i	0.999087	+	0.0427154i	$0.0136009\pi$
$60$	0.185512	+	1.42658i	0.0239495	+	0.184170i
$61$	1.35047	+	2.33909i	0.172910	+	0.299489i	0.939436	−	0.342724i	$-0.111350\pi$
$61$	1.35047	+	2.33909i	0.172910	+	0.299489i	−0.766526	+	0.642213i	$0.778016\pi$
$62$	−0.511103	+	0.885257i	−0.0649102	+	0.112428i
$63$	7.60218	−	4.35704i	0.957785	−	0.548935i
$64$			8.77879i			1.09735i
$65$		0			0
$66$	−4.80075	−	3.69585i	−0.590932	−	0.454928i
$67$	7.28944	−	1.95320i	0.890547	−	0.238621i	0.215595	−	0.976483i	$-0.430831\pi$
$67$	7.28944	−	1.95320i	0.890547	−	0.238621i	0.674952	+	0.737862i	$0.264164\pi$
$68$	−0.0475824	−	0.0274717i	−0.00577022	−	0.00333144i
$69$	0.755216	−	5.66699i	0.0909173	−	0.682226i
$70$	8.14992	+	8.14992i	0.974102	+	0.974102i
$71$	−5.16536	−	1.38405i	−0.613016	−	0.164257i	−0.0610649	−	0.998134i	$-0.519450\pi$
$71$	−5.16536	−	1.38405i	−0.613016	−	0.164257i	−0.551951	+	0.833877i	$0.686116\pi$
$72$	−8.96564	−	0.0284280i	−1.05661	−	0.00335027i
$73$	−3.46215	+	3.46215i	−0.405214	+	0.405214i	−0.880066	−	0.474852i	$-0.842502\pi$
$73$	−3.46215	+	3.46215i	−0.405214	+	0.405214i	0.474852	+	0.880066i	$0.342502\pi$
$74$	5.80168	−	3.34960i	0.674431	−	0.389383i
$75$	−2.66381	−	6.45995i	−0.307590	−	0.745931i
$76$	−0.379503	−	1.41633i	−0.0435320	−	0.162464i
$77$	7.78177			0.886815
$78$		0			0
$79$	−11.1376			−1.25308			−0.626540	−	0.779389i	$-0.715530\pi$
$79$	−11.1376			−1.25308			−0.626540	+	0.779389i	$0.715530\pi$
$80$	−2.62241	−	9.78695i	−0.293194	−	1.09421i
$81$	0.0570734	−	8.99982i	0.00634148	−	0.999980i
$82$	4.33179	−	2.50096i	0.478366	−	0.276185i
$83$	1.84014	−	1.84014i	0.201981	−	0.201981i	−0.598867	−	0.800848i	$-0.704382\pi$
$83$	1.84014	−	1.84014i	0.201981	−	0.201981i	0.800848	+	0.598867i	$0.204382\pi$
$84$	1.11040	−	0.849243i	0.121154	−	0.0926600i
$85$	0.577269	+	0.154679i	0.0626136	+	0.0167773i
$86$	10.8207	+	10.8207i	1.16682	+	1.16682i
$87$	6.40850	+	0.854033i	0.687063	+	0.0915619i
$88$	−6.89568	−	3.98122i	−0.735082	−	0.424400i
$89$	−1.06120	+	0.284349i	−0.112487	+	0.0301409i	−0.314624	−	0.949217i	$-0.601878\pi$
$89$	−1.06120	+	0.284349i	−0.112487	+	0.0301409i	0.202136	+	0.979357i	$0.435212\pi$
$90$	11.4447	−	3.02775i	1.20638	−	0.319153i
$91$		0			0
$92$		−	0.912102i		−	0.0950932i
$93$	−1.24509	−	0.518049i	−0.129110	−	0.0537191i
$94$	−3.98807	+	6.90753i	−0.411338	+	0.712458i
$95$	7.97458	+	13.8124i	0.818175	+	1.41712i
$96$	−2.66469	+	0.346516i	−0.271964	+	0.0353661i
$97$	−3.14829	+	11.7496i	−0.319661	+	1.19299i	0.599911	+	0.800067i	$0.295203\pi$
$97$	−3.14829	+	11.7496i	−0.319661	+	1.19299i	−0.919571	+	0.392923i	$0.871464\pi$
$98$	0.520155	−	1.94125i	0.0525436	−	0.196095i
$99$	4.01839	−	6.90936i	0.403863	−	0.694417i
$100$	−0.557400	−	0.965446i	−0.0557400	−	0.0965446i
$101$	−6.19691	+	10.7334i	−0.616616	+	1.06801i	0.373483	+	0.927637i	$0.378164\pi$
$101$	−6.19691	+	10.7334i	−0.616616	+	1.06801i	−0.990099	+	0.140373i	$0.955170\pi$
$102$	−0.173689	+	0.417450i	−0.0171978	+	0.0413337i
$103$		−	5.68798i		−	0.560453i	−0.959934	−	0.280226i	$-0.909590\pi$
$103$		−	5.68798i		−	0.560453i	0.959934	−	0.280226i	$-0.0904096\pi$
$104$		0			0
$105$	−9.27566	+	12.0487i	−0.905212	+	1.17583i
$106$	17.2818	−	4.63065i	1.67856	−	0.449769i
$107$	−6.72785	−	3.88433i	−0.650406	−	0.375512i	0.138206	−	0.990404i	$-0.455866\pi$
$107$	−6.72785	−	3.88433i	−0.650406	−	0.375512i	−0.788612	+	0.614891i	$0.789200\pi$
$108$	−0.180644	−	1.42445i	−0.0173825	−	0.137067i
$109$	7.18355	+	7.18355i	0.688060	+	0.688060i	0.961803	−	0.273743i	$-0.0882618\pi$
$109$	7.18355	+	7.18355i	0.688060	+	0.688060i	−0.273743	+	0.961803i	$0.588262\pi$
$110$	10.1555	+	2.72116i	0.968291	+	0.259453i
$111$	5.36914	+	7.02022i	0.509616	+	0.666330i
$112$	−6.96202	+	6.96202i	−0.657849	+	0.657849i
$113$	14.7985	−	8.54390i	1.39212	−	0.803743i	0.398573	−	0.917136i	$-0.369505\pi$
$113$	14.7985	−	8.54390i	1.39212	−	0.803743i	0.993550	+	0.113394i	$0.0361721\pi$
$114$	−11.1552	+	4.59994i	−1.04478	+	0.430823i
$115$	2.56778	+	9.58310i	0.239447	+	0.893628i
$116$	1.03145			0.0957674
$117$		0			0
$118$	−4.38317			−0.403504
$119$	−0.150306	−	0.560951i	−0.0137786	−	0.0514223i
$120$	14.3837	−	5.93122i	1.31304	−	0.541444i
$121$	−3.37877	+	1.95074i	−0.307161	+	0.177340i
$122$	2.50742	−	2.50742i	0.227011	−	0.227011i
$123$	4.00884	+	5.24161i	0.361465	+	0.472620i
$124$	−0.207818	−	0.0556848i	−0.0186627	−	0.00500064i
$125$	−2.05245	−	2.05245i	−0.183577	−	0.183577i
$126$	−8.10860	−	8.16019i	−0.722372	−	0.726967i
$127$	8.33573	+	4.81263i	0.739676	+	0.427052i	0.821952	−	0.569557i	$-0.192885\pi$
$127$	8.33573	+	4.81263i	0.739676	+	0.427052i	−0.0822755	+	0.996610i	$0.526219\pi$
$128$	8.13573	−	2.17996i	0.719103	−	0.192683i
$129$	−12.3153	+	15.9971i	−1.08430	+	1.40846i
$130$		0			0
$131$		−	11.9013i		−	1.03982i	−0.854221	−	0.519910i	$-0.825965\pi$
$131$		−	11.9013i		−	1.03982i	0.854221	−	0.519910i	$-0.174035\pi$
$132$	0.489860	−	1.17734i	0.0426368	−	0.102475i
$133$	7.74916	−	13.4219i	0.671937	−	1.16383i
$134$	−4.95390	−	8.58041i	−0.427952	−	0.741234i
$135$	5.90811	+	14.4575i	0.508489	+	1.24431i
$136$	−0.153796	+	0.573976i	−0.0131879	+	0.0492180i
$137$	−4.50231	+	16.8029i	−0.384659	+	1.43557i	0.454045	+	0.890979i	$0.349980\pi$
$137$	−4.50231	+	16.8029i	−0.384659	+	1.43557i	−0.838704	+	0.544587i	$0.816686\pi$
$138$	−7.44322	+	0.967917i	−0.633609	+	0.0823945i
$139$	−1.16453	−	2.01702i	−0.0987737	−	0.171081i	0.812404	−	0.583096i	$-0.198159\pi$
$139$	−1.16453	−	2.01702i	−0.0987737	−	0.171081i	−0.911177	+	0.412014i	$0.864825\pi$
$140$	−1.21294	+	2.10088i	−0.102512	+	0.177557i
$141$	−9.71528	−	4.04226i	−0.818174	−	0.340420i
$142$			7.02076i			0.589169i
$143$		0			0
$144$	2.58644	+	9.77660i	0.215536	+	0.814717i
$145$	−10.8370	+	2.90377i	−0.899964	+	0.241145i
$146$	5.56697	+	3.21409i	0.460725	+	0.266000i
$147$	2.62814	+	0.350240i	0.216765	+	0.0288873i
$148$	0.997033	+	0.997033i	0.0819556	+	0.0819556i
$149$	15.2383	+	4.08308i	1.24837	+	0.334499i	0.821705	−	0.569913i	$-0.193023\pi$
$149$	15.2383	+	4.08308i	1.24837	+	0.334499i	0.426661	+	0.904412i	$0.359690\pi$
$150$	−7.28702	+	5.57320i	−0.594983	+	0.455050i
$151$	−8.56897	+	8.56897i	−0.697333	+	0.697333i	−0.963834	−	0.266502i	$-0.914132\pi$
$151$	−8.56897	+	8.56897i	−0.697333	+	0.697333i	0.266502	+	0.963834i	$0.414132\pi$
$152$	−13.7336	+	7.92908i	−1.11394	+	0.643133i
$153$	−0.575680	−	0.156211i	−0.0465410	−	0.0126289i
$154$	−2.64424	−	9.86845i	−0.213079	−	0.795222i
$155$	2.34023			0.187972
$156$		0			0
$157$	−3.26731			−0.260759			−0.130380	−	0.991464i	$-0.541620\pi$
$157$	−3.26731			−0.260759			−0.130380	+	0.991464i	$0.541620\pi$
$158$	3.78456	+	14.1242i	0.301084	+	1.12366i
$159$	8.99815	+	21.8212i	0.713600	+	1.73054i
$160$	4.03836	−	2.33155i	0.319260	−	0.184325i
$161$	6.81701	−	6.81701i	0.537256	−	0.537256i
$162$	−11.4325	+	2.98576i	−0.898223	+	0.234583i
$163$	−5.62972	−	1.50848i	−0.440954	−	0.118153i	0.0315098	−	0.999503i	$-0.489968\pi$
$163$	−5.62972	−	1.50848i	−0.440954	−	0.118153i	−0.472463	+	0.881350i	$0.656635\pi$
$164$	0.744429	+	0.744429i	0.0581302	+	0.0581302i
$165$	−1.83226	+	13.7489i	−0.142641	+	1.07035i
$166$	−2.95885	−	1.70829i	−0.229651	−	0.132589i
$167$	1.52736	−	0.409254i	0.118190	−	0.0316690i	−0.199239	−	0.979951i	$-0.563847\pi$
$167$	1.52736	−	0.409254i	0.118190	−	0.0316690i	0.317429	+	0.948282i	$0.397180\pi$
$168$	−11.9799	−	9.22274i	−0.924272	−	0.711550i
$169$		0			0
$170$		−	0.784624i		−	0.0601779i
$171$	−7.91567	−	13.8113i	−0.605327	−	1.05618i
$172$	−1.61043	+	2.78934i	−0.122794	+	0.212685i
$173$	6.21160	+	10.7588i	0.472259	+	0.817977i	0.999496	−	0.0317413i	$-0.0101053\pi$
$173$	6.21160	+	10.7588i	0.472259	+	0.817977i	−0.527237	+	0.849718i	$0.676772\pi$
$174$	−1.09456	−	8.41714i	−0.0829787	−	0.638101i
$175$	3.04971	−	11.3817i	0.230537	−	0.860374i
$176$	−2.32454	+	8.67529i	−0.175219	+	0.653925i
$177$	−0.745689	−	5.73431i	−0.0560494	−	0.431017i
$178$	0.721194	+	1.24914i	0.0540557	+	0.0936273i
$179$	8.15142	−	14.1187i	0.609265	−	1.05528i	−0.382096	−	0.924123i	$-0.624798\pi$
$179$	8.15142	−	14.1187i	0.609265	−	1.05528i	0.991362	−	0.131156i	$-0.0418689\pi$
$180$	1.23901	+	2.16182i	0.0923501	+	0.161133i
$181$		−	9.29621i		−	0.690982i	−0.938422	−	0.345491i	$-0.887712\pi$
$181$		−	9.29621i		−	0.690982i	0.938422	−	0.345491i	$-0.112288\pi$
$182$		0			0
$183$	3.70692	+	2.85377i	0.274024	+	0.210957i
$184$	−9.52842	+	2.55313i	−0.702444	+	0.188219i
$185$	−13.2823	−	7.66855i	−0.976535	−	0.563803i
$186$	−0.233881	+	1.75500i	−0.0171490	+	0.128683i
$187$	−0.374590	−	0.374590i	−0.0273928	−	0.0273928i
$188$	−1.62158	−	0.434500i	−0.118266	−	0.0316892i
$189$	9.29612	−	11.9964i	0.676193	−	0.872607i
$190$	14.8064	−	14.8064i	1.07417	−	1.07417i
$191$	1.75656	−	1.01415i	0.127100	−	0.0733813i	−0.435102	−	0.900381i	$-0.643288\pi$
$191$	1.75656	−	1.01415i	0.127100	−	0.0733813i	0.562202	+	0.827000i	$0.309954\pi$
$192$	5.79654	+	14.0571i	0.418329	+	1.01448i
$193$	1.02822	+	3.83737i	0.0740130	+	0.276220i	0.993008	−	0.118050i	$-0.0376642\pi$
$193$	1.02822	+	3.83737i	0.0740130	+	0.276220i	−0.918995	+	0.394270i	$0.870998\pi$
$194$	15.9700			1.14658
$195$		0			0
$196$	0.422998			0.0302142
$197$	1.78323	+	6.65511i	0.127050	+	0.474157i	0.999904	−	0.0138237i	$-0.00440036\pi$
$197$	1.78323	+	6.65511i	0.127050	+	0.474157i	−0.872855	+	0.487981i	$0.837734\pi$
$198$	−10.1276	−	2.74812i	−0.719734	−	0.195300i
$199$	−5.49109	+	3.17028i	−0.389253	+	0.224735i	−0.681836	−	0.731505i	$-0.738818\pi$
$199$	−5.49109	+	3.17028i	−0.389253	+	0.224735i	0.292584	+	0.956240i	$0.405485\pi$
$200$	−8.52542	+	8.52542i	−0.602838	+	0.602838i
$201$	10.3826	−	7.94071i	0.732330	−	0.560094i
$202$	15.7172	+	4.21142i	1.10586	+	0.296315i
$203$	7.70898	+	7.70898i	0.541065	+	0.541065i
$204$	−0.0943309	−	0.0125711i	−0.00660449	−	0.000880151i
$205$	−9.91717	−	5.72568i	−0.692645	−	0.399899i
$206$	−7.21321	+	1.93277i	−0.502568	+	0.134663i
$207$	−2.53256	−	9.57296i	−0.176025	−	0.665367i
$208$		0			0
$209$		−	14.1376i		−	0.977916i
$210$	18.4314	+	7.66880i	1.27189	+	0.529197i
$211$	0.401137	−	0.694790i	0.0276154	−	0.0478313i	−0.851887	−	0.523725i	$-0.824542\pi$
$211$	0.401137	−	0.694790i	0.0276154	−	0.0478313i	0.879503	+	0.475894i	$0.157875\pi$
$212$	1.88286	+	3.26121i	0.129315	+	0.223981i
$213$	−9.18494	+	1.19441i	−0.629342	+	0.0818396i
$214$	−2.63979	+	9.85182i	−0.180452	+	0.673457i
$215$	9.06747	−	33.8402i	0.618396	−	2.30789i
$216$	−14.3751	+	5.87440i	−0.978098	+	0.399702i
$217$	−1.13704	−	1.96941i	−0.0771873	−	0.133692i
$218$	6.66886	−	11.5508i	0.451672	−	0.782319i
$219$	−3.25776	+	7.82981i	−0.220139	+	0.529089i
$220$			2.21289i			0.149193i
$221$		0			0
$222$	7.07826	−	9.19435i	0.475062	−	0.617084i
$223$	2.98478	−	0.799768i	0.199875	−	0.0535565i	−0.157492	−	0.987520i	$-0.550341\pi$
$223$	2.98478	−	0.799768i	0.199875	−	0.0535565i	0.357368	+	0.933964i	$0.383674\pi$
$224$	−3.92421	−	2.26564i	−0.262197	−	0.151380i
$225$	−8.53087	−	8.58514i	−0.568725	−	0.572343i
$226$	−15.8635	−	15.8635i	−1.05522	−	1.05522i
$227$	−25.0314	−	6.70715i	−1.66139	−	0.445169i	−0.698624	−	0.715489i	$-0.746204\pi$
$227$	−25.0314	−	6.70715i	−1.66139	−	0.445169i	−0.962770	+	0.270320i	$0.912870\pi$
$228$	−1.54287	−	2.01732i	−0.102179	−	0.133600i
$229$	19.6410	−	19.6410i	1.29791	−	1.29791i	0.368147	−	0.929768i	$-0.379992\pi$
$229$	19.6410	−	19.6410i	1.29791	−	1.29791i	0.929768	−	0.368147i	$-0.120008\pi$
$230$	11.2803	−	6.51267i	0.743799	−	0.429433i
$231$	12.4606	−	5.13822i	0.819847	−	0.338070i
$232$	−2.88720	−	10.7752i	−0.189554	−	0.707425i
$233$	−14.4551			−0.946988			−0.473494	−	0.880797i	$-0.657007\pi$
$233$	−14.4551			−0.946988			−0.473494	+	0.880797i	$0.657007\pi$
$234$		0			0
$235$	18.2605			1.19118
$236$	−0.238774	−	0.891116i	−0.0155428	−	0.0580067i
$237$	−17.8342	+	7.35405i	−1.15845	+	0.477697i
$238$	−0.660297	+	0.381222i	−0.0428007	+	0.0247110i
$239$	4.24248	−	4.24248i	0.274423	−	0.274423i	−0.556455	−	0.830878i	$-0.687839\pi$
$239$	4.24248	−	4.24248i	0.274423	−	0.274423i	0.830878	+	0.556455i	$0.187839\pi$
$240$	−10.6614	−	13.9399i	−0.688188	−	0.899814i
$241$	−23.8375	−	6.38724i	−1.53551	−	0.411438i	−0.610697	−	0.791864i	$-0.709111\pi$
$241$	−23.8375	−	6.38724i	−1.53551	−	0.411438i	−0.924811	+	0.380426i	$0.875777\pi$
$242$	3.62193	+	3.62193i	0.232827	+	0.232827i
$243$	−5.85110	−	14.4487i	−0.375348	−	0.926884i
$244$	0.646361	+	0.373177i	0.0413790	+	0.0238902i
$245$	−4.44427	+	1.19084i	−0.283934	+	0.0760799i
$246$	5.28494	−	6.86491i	0.336956	−	0.437691i
$247$		0			0
$248$			2.32688i			0.147757i
$249$	1.73151	−	4.16156i	0.109730	−	0.263728i
$250$	−1.90540	+	3.30024i	−0.120508	+	0.208726i
$251$	−10.8649	−	18.8186i	−0.685789	−	1.18782i	−0.973188	−	0.230010i	$-0.926124\pi$
$251$	−10.8649	−	18.8186i	−0.685789	−	1.18782i	0.287400	−	0.957811i	$-0.407209\pi$
$252$	1.21728	−	2.09304i	0.0766814	−	0.131849i
$253$	2.27612	−	8.49459i	0.143098	−	0.534051i
$254$	3.27066	−	12.2063i	0.205220	−	0.765891i
$255$	1.02649	−	0.133484i	0.0642812	−	0.00835912i
$256$	3.24975	+	5.62873i	0.203109	+	0.351796i
$257$	−8.15559	+	14.1259i	−0.508732	+	0.881149i	0.491217	+	0.871037i	$0.336552\pi$
$257$	−8.15559	+	14.1259i	−0.508732	+	0.881149i	−0.999949	+	0.0101119i	$0.996781\pi$
$258$	24.4714	+	10.1819i	1.52353	+	0.633897i
$259$			14.9036i			0.926062i
$260$		0			0
$261$	10.8255	−	2.86394i	0.670084	−	0.177273i
$262$	−15.0926	+	4.04406i	−0.932426	+	0.249843i
$263$	9.95602	+	5.74811i	0.613914	+	0.354444i	0.774496	−	0.632579i	$-0.218004\pi$
$263$	9.95602	+	5.74811i	0.613914	+	0.354444i	−0.160582	+	0.987023i	$0.551337\pi$
$264$	−13.6705	−	1.82181i	−0.841361	−	0.112125i
$265$	−28.9635	−	28.9635i	−1.77922	−	1.77922i
$266$	−19.6542	−	5.26633i	−1.20508	−	0.322899i
$267$	−1.51151	+	1.15602i	−0.0925026	+	0.0707470i
$268$	1.47457	−	1.47457i	0.0900734	−	0.0900734i
$269$	−9.64658	+	5.56946i	−0.588162	+	0.339576i	−0.764371	−	0.644777i	$-0.776950\pi$
$269$	−9.64658	+	5.56946i	−0.588162	+	0.339576i	0.176208	+	0.984353i	$0.443617\pi$
$270$	16.3268	−	12.4050i	0.993615	−	0.754947i
$271$	1.57276	+	5.86962i	0.0955383	+	0.356554i	0.997101	−	0.0760956i	$-0.0242454\pi$
$271$	1.57276	+	5.86962i	0.0955383	+	0.356554i	−0.901562	+	0.432650i	$0.857579\pi$
$272$	0.670260			0.0406405
$273$		0			0
$274$	22.8384			1.37972
$275$	−2.78195	−	10.3824i	−0.167758	−	0.626080i
$276$	−0.602251	−	1.46051i	−0.0362513	−	0.0879123i
$277$	24.0591	−	13.8905i	1.44557	−	0.834600i	0.447356	−	0.894356i	$-0.352366\pi$
$277$	24.0591	−	13.8905i	1.44557	−	0.834600i	0.998213	+	0.0597558i	$0.0190322\pi$
$278$	−2.16218	+	2.16218i	−0.129679	+	0.129679i
$279$	−2.33577	−	0.00740621i	−0.139839	−	0.000443398i
$280$	25.3424	+	6.79047i	1.51450	+	0.405808i
$281$	−11.6187	−	11.6187i	−0.693113	−	0.693113i	0.269803	−	0.962916i	$-0.413042\pi$
$281$	−11.6187	−	11.6187i	−0.693113	−	0.693113i	−0.962916	+	0.269803i	$0.913042\pi$
$282$	−1.82494	+	13.6940i	−0.108674	+	0.815466i
$283$	23.0251	+	13.2935i	1.36870	+	0.790219i	0.990762	−	0.135612i	$-0.0432999\pi$
$283$	23.0251	+	13.2935i	1.36870	+	0.790219i	0.377938	+	0.925831i	$0.376633\pi$
$284$	−1.42735	+	0.382456i	−0.0846974	+	0.0226946i
$285$	21.8895	+	16.8516i	1.29662	+	0.998203i
$286$		0			0
$287$			11.1277i			0.656845i
$288$	−4.03804	+	2.31433i	−0.237944	+	0.136373i
$289$	8.48023	−	14.6882i	0.498837	−	0.864011i
$290$	7.36482	+	12.7563i	0.432477	+	0.749073i
$291$	2.71691	+	20.8929i	0.159268	+	1.22476i
$292$	−0.350176	+	1.30687i	−0.0204925	+	0.0764790i
$293$	−0.749260	+	2.79628i	−0.0437722	+	0.163360i	−0.984352	−	0.176212i	$-0.943616\pi$
$293$	−0.749260	+	2.79628i	−0.0437722	+	0.163360i	0.940580	+	0.339572i	$0.110282\pi$
$294$	−0.448883	−	3.45188i	−0.0261794	−	0.201318i
$295$	5.01740	+	8.69039i	0.292124	+	0.505974i
$296$	7.62480	−	13.2065i	0.443182	−	0.767614i
$297$	1.87228	−	13.7170i	0.108641	−	0.795938i
$298$		−	20.7118i		−	1.19980i
$299$		0			0
$300$	−1.53001	−	1.17788i	−0.0883354	−	0.0680049i
$301$	−32.8837	+	8.81115i	−1.89538	+	0.507866i
$302$	13.7785	+	7.95501i	0.792862	+	0.457759i
$303$	−2.83571	+	21.2786i	−0.162907	+	1.22242i
$304$	12.6483	+	12.6483i	0.725429	+	0.725429i
$305$	−7.84164	−	2.10116i	−0.449011	−	0.120312i
$306$	−0.00248313	+	0.783129i	−0.000141951	+	0.0447685i
$307$	−13.9565	+	13.9565i	−0.796541	+	0.796541i	−0.982548	−	0.186007i	$-0.940445\pi$
$307$	−13.9565	+	13.9565i	−0.796541	+	0.796541i	0.186007	+	0.982548i	$0.440445\pi$
$308$	1.86225	−	1.07517i	0.106111	−	0.0612635i
$309$	−3.75571	−	9.10790i	−0.213655	−	0.518130i
$310$	−0.795211	−	2.96777i	−0.0451649	−	0.168558i
$311$	−26.9755			−1.52964			−0.764821	−	0.644243i	$-0.777172\pi$
$311$	−26.9755			−1.52964			−0.764821	+	0.644243i	$0.777172\pi$
$312$		0			0
$313$	−23.9660			−1.35464			−0.677320	−	0.735689i	$-0.736859\pi$
$313$	−23.9660			−1.35464			−0.677320	+	0.735689i	$0.736859\pi$
$314$	1.11023	+	4.14344i	0.0626539	+	0.233828i
$315$	−6.89709	+	25.4176i	−0.388607	+	1.43212i
$316$	−2.66533	+	1.53883i	−0.149937	+	0.0865660i
$317$	−21.6899	+	21.6899i	−1.21823	+	1.21823i	−0.249973	+	0.968253i	$0.580422\pi$
$317$	−21.6899	+	21.6899i	−1.21823	+	1.21823i	−0.968253	+	0.249973i	$0.919578\pi$
$318$	24.6151	−	18.8259i	1.38034	−	1.05570i
$319$	9.60608	+	2.57394i	0.537837	+	0.144113i
$320$	−18.6581	−	18.6581i	−1.04302	−	1.04302i
$321$	−13.3378	−	1.77747i	−0.744443	−	0.0992087i
$322$	−10.9614	−	6.32857i	−0.610856	−	0.352678i
$323$	−1.01911	+	0.273070i	−0.0567049	+	0.0151940i
$324$	−1.22980	−	2.16162i	−0.0683224	−	0.120090i
$325$		0			0
$326$			7.65191i			0.423800i
$327$	16.2459	+	6.75948i	0.898402	+	0.373800i
$328$	5.69301	−	9.86058i	0.314344	−	0.544460i
$329$	−8.87216	−	15.3670i	−0.489138	−	0.847212i
$330$	18.0583	−	2.34831i	0.994079	−	0.129270i
$331$	−0.171746	+	0.640966i	−0.00944003	+	0.0352307i	−0.970485	−	0.241161i	$-0.922472\pi$
$331$	−0.171746	+	0.640966i	−0.00944003	+	0.0352307i	0.961045	+	0.276391i	$0.0891386\pi$
$332$	0.186119	−	0.694605i	0.0102146	−	0.0381214i
$333$	13.2327	+	7.69597i	0.725150	+	0.421737i
$334$	−1.03799	−	1.79785i	−0.0567964	−	0.0983742i
$335$	−11.3414	+	19.6439i	−0.619648	+	1.07326i
$336$	−6.55102	+	15.7449i	−0.357388	+	0.858956i
$337$		−	25.0872i		−	1.36659i	−0.730143	−	0.683294i	$-0.760547\pi$
$337$		−	25.0872i		−	1.36659i	0.730143	−	0.683294i	$-0.239453\pi$
$338$		0			0
$339$	18.0547	−	23.4522i	0.980596	−	1.27375i
$340$	0.159517	−	0.0427425i	0.00865103	−	0.00231804i
$341$	−1.79650	−	1.03721i	−0.0972858	−	0.0561680i
$342$	−14.8251	+	14.7313i	−0.801647	+	0.796580i
$343$	−11.2955	−	11.2955i	−0.609900	−	0.609900i
$344$	33.6472	+	9.01573i	1.81413	+	0.486096i
$345$	10.4393	+	13.6495i	0.562033	+	0.734864i
$346$	11.5331	−	11.5331i	0.620023	−	0.620023i
$347$	−14.2117	+	8.20511i	−0.762923	+	0.440474i	−0.830344	−	0.557251i	$-0.811856\pi$
$347$	−14.2117	+	8.20511i	−0.762923	+	0.440474i	0.0674214	+	0.997725i	$0.478523\pi$
$348$	1.65161	−	0.681053i	0.0885356	−	0.0365083i
$349$	−7.75800	−	28.9532i	−0.415276	−	1.54983i	−0.784282	−	0.620405i	$-0.786968\pi$
$349$	−7.75800	−	28.9532i	−0.415276	−	1.54983i	0.369006	−	0.929427i	$-0.379698\pi$
$350$	−15.4700			−0.826905
$351$		0			0
$352$	−4.13344			−0.220313
$353$	1.74394	+	6.50846i	0.0928203	+	0.346410i	0.996680	−	0.0814189i	$-0.0259452\pi$
$353$	1.74394	+	6.50846i	0.0928203	+	0.346410i	−0.903860	+	0.427829i	$0.859279\pi$
$354$	−7.01858	+	2.89416i	−0.373033	+	0.153823i
$355$	13.9199	−	8.03664i	0.738790	−	0.426540i
$356$	−0.214669	+	0.214669i	−0.0113774	+	0.0113774i
$357$	−0.611069	−	0.798980i	−0.0323412	−	0.0422865i
$358$	−20.6744	−	5.53970i	−1.09268	−	0.292782i
$359$	6.76884	+	6.76884i	0.357246	+	0.357246i	0.862797	−	0.505551i	$-0.168711\pi$
$359$	6.76884	+	6.76884i	0.357246	+	0.357246i	−0.505551	+	0.862797i	$0.668711\pi$
$360$	19.1156	−	18.9948i	1.00748	−	1.00111i
$361$	−7.92989	−	4.57832i	−0.417363	−	0.240964i
$362$	−11.7890	+	3.15885i	−0.619616	+	0.166025i
$363$	−4.12223	+	5.35459i	−0.216361	+	0.281043i
$364$		0			0
$365$		−	14.7166i		−	0.770303i
$366$	2.35940	−	5.67065i	0.123328	−	0.296410i
$367$	6.01337	−	10.4155i	0.313895	−	0.543682i	−0.665307	−	0.746570i	$-0.731699\pi$
$367$	6.01337	−	10.4155i	0.313895	−	0.543682i	0.979202	+	0.202888i	$0.0650326\pi$
$368$	5.56341	+	9.63611i	0.290013	+	0.502317i
$369$	9.88015	+	5.74615i	0.514340	+	0.299133i
$370$	−5.21154	+	19.4497i	−0.270935	+	1.01114i
$371$	−10.3017	+	38.4465i	−0.534838	+	1.99604i
$372$	−0.369539	+	0.0480548i	−0.0191597	+	0.00249152i
$373$	−6.67932	−	11.5689i	−0.345842	−	0.599016i	0.639664	−	0.768654i	$-0.279073\pi$
$373$	−6.67932	−	11.5689i	−0.345842	−	0.599016i	−0.985506	+	0.169638i	$0.945740\pi$
$374$	−0.347751	+	0.602323i	−0.0179818	+	0.0311454i
$375$	−4.64172	−	1.93129i	−0.239697	−	0.0997313i
$376$			18.1563i			0.936340i
$377$		0			0
$378$	−18.3720	−	7.71252i	−0.944955	−	0.396689i
$379$	29.9123	−	8.01497i	1.53649	−	0.411701i	0.611360	−	0.791352i	$-0.290623\pi$
$379$	29.9123	−	8.01497i	1.53649	−	0.411701i	0.925130	+	0.379651i	$0.123956\pi$
$380$	3.81678	+	2.20362i	0.195797	+	0.113043i
$381$	16.5254	+	2.20226i	0.846620	+	0.112825i
$382$	−1.88297	−	1.88297i	−0.0963413	−	0.0963413i
$383$	9.90441	+	2.65388i	0.506092	+	0.135607i	0.502826	−	0.864388i	$-0.332294\pi$
$383$	9.90441	+	2.65388i	0.506092	+	0.135607i	0.00326604	+	0.999995i	$0.498960\pi$
$384$	11.5880	−	8.86261i	0.591346	−	0.452268i
$385$	−16.5390	+	16.5390i	−0.842908	+	0.842908i
$386$	4.51698	−	2.60788i	0.229908	−	0.132738i
$387$	−9.15729	+	33.7471i	−0.465491	+	1.71546i
$388$	0.869969	+	3.24677i	0.0441660	+	0.164830i
$389$	30.1074			1.52650			0.763252	−	0.646101i	$-0.223602\pi$
$389$	30.1074			1.52650			0.763252	+	0.646101i	$0.223602\pi$
$390$		0			0
$391$	−0.656299			−0.0331905
$392$	−1.18405	−	4.41892i	−0.0598033	−	0.223189i
$393$	−7.85830	−	19.0570i	−0.396399	−	0.961299i
$394$	7.83374	−	4.52281i	0.394658	−	0.227856i
$395$	23.6714	−	23.6714i	1.19104	−	1.19104i
$396$	0.00700321	−	2.20868i	0.000351925	−	0.110990i
$397$	3.31510	+	0.888280i	0.166380	+	0.0445815i	0.341048	−	0.940046i	$-0.389218\pi$
$397$	3.31510	+	0.888280i	0.166380	+	0.0445815i	−0.174667	+	0.984628i	$0.555885\pi$
$398$	5.88626	+	5.88626i	0.295052	+	0.295052i
$399$	3.54602	−	26.6086i	0.177523	−	1.33210i
$400$	11.7776	+	6.79978i	0.588878	+	0.339989i
$401$	19.2725	−	5.16404i	0.962421	−	0.257880i	0.256796	−	0.966466i	$-0.417333\pi$
$401$	19.2725	−	5.16404i	0.962421	−	0.257880i	0.705625	+	0.708586i	$0.250666\pi$
$402$	−13.5980	−	10.4684i	−0.678207	−	0.522117i
$403$		0			0
$404$			3.42479i			0.170390i
$405$	19.0065	+	19.2491i	0.944443	+	0.956498i
$406$	7.15664	−	12.3957i	0.355178	−	0.615186i
$407$	6.79751	+	11.7736i	0.336940	+	0.583598i
$408$	0.132723	+	1.02063i	0.00657076	+	0.0505288i
$409$	−1.43417	+	5.35240i	−0.0709152	+	0.264659i	−0.992276	−	0.124049i	$-0.960412\pi$
$409$	−1.43417	+	5.35240i	−0.0709152	+	0.264659i	0.921361	+	0.388708i	$0.127079\pi$
$410$	−3.89117	+	14.5220i	−0.192171	+	0.717193i
$411$	3.88540	+	29.8785i	0.191653	+	1.47380i
$412$	−0.785880	−	1.36118i	−0.0387175	−	0.0670608i
$413$	4.87557	−	8.44474i	0.239911	−	0.415538i
$414$	−11.2794	+	6.46456i	−0.554352	+	0.317716i
$415$			7.82191i			0.383962i
$416$		0			0
$417$	−3.19652	−	2.46083i	−0.156534	−	0.120508i
$418$	−17.9286	+	4.80394i	−0.876914	+	0.234969i
$419$	29.8207	+	17.2170i	1.45684	+	0.841106i	0.998854	−	0.0478553i	$-0.0152386\pi$
$419$	29.8207	+	17.2170i	1.45684	+	0.841106i	0.457983	+	0.888961i	$0.348572\pi$
$420$	−0.555043	+	4.16493i	−0.0270833	+	0.203228i
$421$	18.6143	+	18.6143i	0.907208	+	0.907208i	0.996046	−	0.0888383i	$-0.0283154\pi$
$421$	18.6143	+	18.6143i	0.907208	+	0.907208i	−0.0888383	+	0.996046i	$0.528315\pi$
$422$	−1.01740	−	0.272613i	−0.0495265	−	0.0132706i
$423$	−18.2257	−	0.0577896i	−0.886164	−	0.00280983i
$424$	28.7983	−	28.7983i	1.39857	−	1.39857i
$425$	−0.694683	+	0.401075i	−0.0336971	+	0.0194550i
$426$	4.63573	+	11.2420i	0.224602	+	0.544678i
$427$	2.04177	+	7.61997i	0.0988080	+	0.368756i
$428$	−2.14672			−0.103765
$429$		0			0
$430$	−45.9956			−2.21811
$431$	−2.92686	−	10.9232i	−0.140982	−	0.526152i	−0.999901	−	0.0140414i	$-0.995530\pi$
$431$	−2.92686	−	10.9232i	−0.140982	−	0.526152i	0.858919	−	0.512111i	$-0.171136\pi$
$432$	10.5969	+	13.9470i	0.509845	+	0.671027i
$433$	5.37469	−	3.10308i	0.258291	−	0.149124i	−0.365264	−	0.930904i	$-0.619021\pi$
$433$	5.37469	−	3.10308i	0.258291	−	0.149124i	0.623555	+	0.781780i	$0.285688\pi$
$434$	−2.11114	+	2.11114i	−0.101338	+	0.101338i
$435$	−15.4355	+	11.8052i	−0.740075	+	0.566017i
$436$	2.71161	+	0.726573i	0.129862	+	0.0347965i
$437$	−12.3848	−	12.3848i	−0.592447	−	0.592447i
$438$	11.0364	+	1.47077i	0.527338	+	0.0702760i
$439$	−33.5869	−	19.3914i	−1.60301	−	0.925501i	−0.990880	−	0.134748i	$-0.956978\pi$
$439$	−33.5869	−	19.3914i	−1.60301	−	0.925501i	−0.612135	−	0.790753i	$-0.709689\pi$
$440$	23.1173	−	6.19427i	1.10208	−	0.295300i
$441$	4.43957	−	1.17451i	0.211408	−	0.0559288i
$442$		0			0
$443$			18.3132i			0.870087i	0.900409	+	0.435043i	$0.143267\pi$
$443$			18.3132i			0.870087i	−0.900409	+	0.435043i	$0.856733\pi$
$444$	2.25484	+	0.938174i	0.107010	+	0.0445238i
$445$	1.65110	−	2.85978i	0.0782694	−	0.135567i
$446$	−2.02845	−	3.51338i	−0.0960500	−	0.166364i
$447$	27.0963	−	3.52361i	1.28161	−	0.166661i
$448$	−6.63628	+	24.7669i	−0.313535	+	1.17013i
$449$	0.501884	−	1.87306i	0.0236854	−	0.0883950i	−0.953071	−	0.302745i	$-0.902097\pi$
$449$	0.501884	−	1.87306i	0.0236854	−	0.0883950i	0.976757	+	0.214350i	$0.0687635\pi$
$450$	−7.98846	+	13.7357i	−0.376580	+	0.647505i
$451$	5.07532	+	8.79072i	0.238988	+	0.413939i
$452$	2.36094	−	4.08927i	0.111049	−	0.192343i
$453$	−8.06311	+	19.3791i	−0.378838	+	0.910510i
$454$			34.0227i			1.59676i
$455$		0			0
$456$	−16.7555	+	21.7646i	−0.784646	+	1.01922i
$457$	−5.62868	+	1.50820i	−0.263299	+	0.0705507i	−0.388053	−	0.921637i	$-0.626852\pi$
$457$	−5.62868	+	1.50820i	−0.263299	+	0.0705507i	0.124755	+	0.992188i	$0.460186\pi$
$458$	−31.5818	−	18.2337i	−1.47572	−	0.852007i
$459$	−1.02495	+	0.129982i	−0.0478408	+	0.00606702i
$460$	1.93854	+	1.93854i	0.0903851	+	0.0903851i
$461$	13.8221	+	3.70361i	0.643758	+	0.172494i	0.565905	−	0.824470i	$-0.308527\pi$
$461$	13.8221	+	3.70361i	0.643758	+	0.172494i	0.0778529	+	0.996965i	$0.475194\pi$
$462$	−10.7501	−	14.0559i	−0.500142	−	0.653942i
$463$	−2.99038	+	2.99038i	−0.138975	+	0.138975i	−0.773172	−	0.634197i	$-0.781331\pi$
$463$	−2.99038	+	2.99038i	−0.138975	+	0.138975i	0.634197	+	0.773172i	$0.281331\pi$
$464$	−10.8969	+	6.29136i	−0.505878	+	0.292069i
$465$	3.74731	−	1.54523i	0.173777	−	0.0716584i
$466$	4.91185	+	18.3313i	0.227537	+	0.849181i
$467$	37.5105			1.73578			0.867888	−	0.496759i	$-0.165477\pi$
$467$	37.5105			1.73578			0.867888	+	0.496759i	$0.165477\pi$
$468$		0			0
$469$	22.0417			1.01779
$470$	−6.20491	−	23.1571i	−0.286211	−	1.06816i
$471$	−5.23179	+	2.15737i	−0.241068	+	0.0994063i
$472$	−8.64081	+	4.98877i	−0.397726	+	0.229627i
$473$	−21.9589	+	21.9589i	−1.00967	+	1.00967i
$474$	15.3861	+	20.1175i	0.706707	+	0.924028i
$475$	−20.6777	−	5.54058i	−0.948759	−	0.254219i
$476$	−0.113474	−	0.113474i	−0.00520106	−	0.00520106i
$477$	28.8167	+	29.0000i	1.31942	+	1.32782i
$478$	−6.82169	−	3.93851i	−0.312017	−	0.180143i
$479$	1.97272	−	0.528588i	0.0901358	−	0.0241518i	−0.213469	−	0.976950i	$-0.568476\pi$
$479$	1.97272	−	0.528588i	0.0901358	−	0.0241518i	0.303605	+	0.952798i	$0.401810\pi$
$480$	4.92695	−	6.39989i	0.224883	−	0.292114i
$481$		0			0
$482$			32.3999i			1.47578i
$483$	6.41457	−	15.4170i	0.291873	−	0.701496i
$484$	−0.539048	+	0.933658i	−0.0245022	+	0.0424390i
$485$	−18.2808	−	31.6633i	−0.830090	−	1.43776i
$486$	−16.3349	+	12.3297i	−0.740967	+	0.559288i
$487$	6.49144	−	24.2264i	0.294155	−	1.09780i	−0.647731	−	0.761869i	$-0.724282\pi$
$487$	6.49144	−	24.2264i	0.294155	−	1.09780i	0.941886	−	0.335933i	$-0.109052\pi$
$488$	2.08917	−	7.79690i	0.0945724	−	0.352949i
$489$	−10.0106	+	1.30178i	−0.452697	+	0.0588687i
$490$	3.02033	+	5.23136i	0.136444	+	0.236329i
$491$	3.76608	−	6.52305i	0.169961	−	0.294381i	−0.768445	−	0.639916i	$-0.778969\pi$
$491$	3.76608	−	6.52305i	0.169961	−	0.294381i	0.938406	+	0.345535i	$0.112302\pi$
$492$	1.68356	+	0.700482i	0.0759007	+	0.0315802i
$493$		−	0.742173i		−	0.0334258i
$494$		0			0
$495$	6.14436	+	23.2254i	0.276169	+	1.04390i
$496$	2.53520	−	0.679304i	0.113834	−	0.0305016i
$497$	−13.5264	−	7.80946i	−0.606741	−	0.350302i
$498$	−5.86584	−	0.781716i	−0.262855	−	0.0350295i
$499$	8.71539	+	8.71539i	0.390154	+	0.390154i	0.874742	−	0.484588i	$-0.161030\pi$
$499$	8.71539	+	8.71539i	0.390154	+	0.390154i	−0.484588	+	0.874742i	$0.661030\pi$
$500$	−0.774749	−	0.207593i	−0.0346478	−	0.00928385i
$501$	2.17546	−	1.66382i	0.0971925	−	0.0743339i
$502$	−20.1729	+	20.1729i	−0.900362	+	0.900362i
$503$	−2.03490	+	1.17485i	−0.0907316	+	0.0523839i	−0.544679	−	0.838644i	$-0.683349\pi$
$503$	−2.03490	+	1.17485i	−0.0907316	+	0.0523839i	0.453948	+	0.891028i	$0.350015\pi$
$504$	−25.2726	−	6.85774i	−1.12573	−	0.305468i
$505$	−9.64160	−	35.9829i	−0.429046	−	1.60122i
$506$	−11.5458			−0.513276
$507$		0			0
$508$	2.65975			0.118008
$509$	−7.75830	−	28.9544i	−0.343881	−	1.28338i	−0.893914	−	0.448238i	$-0.852052\pi$
$509$	−7.75830	−	28.9544i	−0.343881	−	1.28338i	0.550034	−	0.835142i	$-0.314615\pi$
$510$	−0.518079	−	1.25638i	−0.0229409	−	0.0556336i
$511$	−12.3847	+	7.15031i	−0.547867	+	0.316311i
$512$	17.9453	−	17.9453i	0.793080	−	0.793080i
$513$	−21.7945	−	16.8888i	−0.962249	−	0.745658i
$514$	20.6850	+	5.54254i	0.912377	+	0.244471i
$515$	12.0890	+	12.0890i	0.532705	+	0.532705i
$516$	−0.736932	+	5.52980i	−0.0324416	+	0.243436i
$517$	−14.0178	−	8.09318i	−0.616502	−	0.355938i
$518$	18.9000	−	5.06423i	0.830416	−	0.222509i
$519$	17.0503	+	13.1261i	0.748424	+	0.576174i
$520$		0			0
$521$			5.94611i			0.260504i	0.991481	+	0.130252i	$0.0415786\pi$
$521$			5.94611i			0.260504i	−0.991481	+	0.130252i	$0.958421\pi$
$522$	−7.31042	−	12.7553i	−0.319968	−	0.558282i
$523$	0.429973	−	0.744735i	0.0188014	−	0.0325650i	−0.856472	−	0.516194i	$-0.827348\pi$
$523$	0.429973	−	0.744735i	0.0188014	−	0.0325650i	0.875273	+	0.483629i	$0.160682\pi$
$524$	−1.64434	−	2.84809i	−0.0718335	−	0.124419i
$525$	−2.63184	−	20.2387i	−0.114863	−	0.883288i
$526$	3.90641	−	14.5789i	0.170328	−	0.635672i
$527$	−0.0400678	+	0.149535i	−0.00174538	+	0.00651385i
$528$	2.00603	+	15.4262i	0.0873011	+	0.671340i
$529$	6.05247	+	10.4832i	0.263151	+	0.455791i
$530$	−26.8883	+	46.5719i	−1.16795	+	2.02295i
$531$	−4.98034	−	8.68971i	−0.216128	−	0.377102i
$532$		−	4.28266i		−	0.185677i
$533$		0			0
$534$	1.97961	+	1.52400i	0.0856662	+	0.0659500i
$535$	22.5547	−	6.04351i	0.975124	−	0.261284i
$536$	−19.5318	−	11.2767i	−0.843647	−	0.487080i
$537$	3.73009	−	27.9899i	0.160965	−	1.20785i
$538$	10.3408	+	10.3408i	0.445824	+	0.445824i
$539$	3.93947	+	1.05558i	0.169685	+	0.0454669i
$540$	3.41139	+	2.64353i	0.146803	+	0.113759i
$541$	−5.67009	+	5.67009i	−0.243776	+	0.243776i	−0.818410	−	0.574634i	$-0.805144\pi$
$541$	−5.67009	+	5.67009i	−0.243776	+	0.243776i	0.574634	+	0.818410i	$0.305144\pi$
$542$	6.90914	−	3.98899i	0.296773	−	0.171342i
$543$	−6.13819	−	14.8856i	−0.263415	−	0.638802i
$544$	0.0798382	+	0.297960i	0.00342303	+	0.0127749i
$545$	−30.5353			−1.30799
$546$		0			0
$547$	−29.3587			−1.25529			−0.627643	−	0.778501i	$-0.715980\pi$
$547$	−29.3587			−1.25529			−0.627643	+	0.778501i	$0.715980\pi$
$548$	1.24413	+	4.64314i	0.0531465	+	0.198345i
$549$	7.82005	+	2.12197i	0.333751	+	0.0905636i
$550$	−12.2211	+	7.05585i	−0.521109	+	0.300863i
$551$	14.0053	−	14.0053i	0.596647	−	0.596647i
$552$	−13.5716	+	10.3797i	−0.577647	+	0.441791i
$553$	−31.4217	−	8.41943i	−1.33619	−	0.358031i
$554$	−25.7905	−	25.7905i	−1.09573	−	1.09573i
$555$	−26.3318	−	3.50913i	−1.11772	−	0.148954i
$556$	−0.557363	−	0.321794i	−0.0236375	−	0.0136471i
$557$	−36.1240	+	9.67941i	−1.53062	+	0.410130i	−0.923223	−	0.384265i	$-0.874455\pi$
$557$	−36.1240	+	9.67941i	−1.53062	+	0.410130i	−0.607402	+	0.794395i	$0.707788\pi$
$558$	0.784303	+	2.96463i	0.0332022	+	0.125503i
$559$		0			0
$560$		−	29.5936i		−	1.25056i
$561$	−0.847152	−	0.352477i	−0.0357668	−	0.0148816i
$562$	−10.7862	+	18.6823i	−0.454989	+	0.788064i
$563$	−6.70261	−	11.6093i	−0.282481	−	0.489272i	0.689514	−	0.724272i	$-0.257824\pi$
$563$	−6.70261	−	11.6093i	−0.282481	−	0.489272i	−0.971995	+	0.235000i	$0.924491\pi$
$564$	−2.88346	+	0.374965i	−0.121415	+	0.0157889i
$565$	−13.2932	+	49.6109i	−0.559250	+	2.08715i
$566$	9.03429	−	33.7164i	0.379740	−	1.41721i
$567$	6.96439	−	25.3474i	0.292477	−	1.06449i
$568$	7.99078	+	13.8404i	0.335286	+	0.580732i
$569$	11.3396	−	19.6407i	0.475380	−	0.823382i	−0.524223	−	0.851581i	$-0.675644\pi$
$569$	11.3396	−	19.6407i	0.475380	−	0.823382i	0.999602	+	0.0281995i	$0.00897737\pi$
$570$	13.9323	−	33.4854i	0.583561	−	1.40255i
$571$		−	21.9369i		−	0.918032i	−0.888428	−	0.459016i	$-0.848202\pi$
$571$		−	21.9369i		−	0.918032i	0.888428	−	0.459016i	$-0.151798\pi$
$572$		0			0
$573$	2.14307	−	2.78375i	0.0895279	−	0.116293i
$574$	14.1115	−	3.78118i	0.589004	−	0.157823i
$575$	−11.5322	−	6.65814i	−0.480928	−	0.277664i
$576$	18.5635	+	18.6816i	0.773478	+	0.778399i
$577$	−18.7633	−	18.7633i	−0.781126	−	0.781126i	0.198895	−	0.980021i	$-0.436265\pi$
$577$	−18.7633	−	18.7633i	−0.781126	−	0.781126i	−0.980021	+	0.198895i	$0.936265\pi$
$578$	−21.5084	−	5.76316i	−0.894632	−	0.239716i
$579$	4.18022	+	5.46569i	0.173724	+	0.227146i
$580$	−2.19219	+	2.19219i	−0.0910259	+	0.0910259i
$581$	6.58249	−	3.80040i	0.273088	−	0.157667i
$582$	25.5721	−	10.5448i	1.06000	−	0.437098i
$583$	9.39722	+	35.0709i	0.389193	+	1.45249i
$584$	14.6327			0.605504
$585$		0			0
$586$	3.80070			0.157005
$587$	3.16920	+	11.8276i	0.130807	+	0.488178i	0.999980	−	0.00632980i	$-0.00201485\pi$
$587$	3.16920	+	11.8276i	0.130807	+	0.488178i	−0.869173	+	0.494508i	$0.835348\pi$
$588$	0.677328	−	0.279301i	0.0279325	−	0.0115182i
$589$	−3.57794	+	2.06572i	−0.147426	+	0.0851166i
$590$	9.31581	−	9.31581i	0.383526	−	0.383526i
$591$	7.24970	+	9.47908i	0.298213	+	0.389917i
$592$	−16.6148	−	4.45193i	−0.682865	−	0.182973i
$593$	32.4467	+	32.4467i	1.33243	+	1.33243i	0.903194	+	0.429232i	$0.141216\pi$
$593$	32.4467	+	32.4467i	1.33243	+	1.33243i	0.429232	+	0.903194i	$0.358784\pi$
$594$	−18.0314	+	2.28668i	−0.739836	+	0.0938237i
$595$	1.51168	+	0.872768i	0.0619728	+	0.0357800i
$596$	4.21079	−	1.12828i	0.172481	−	0.0462161i
$597$	−6.69933	+	8.70213i	−0.274185	+	0.356155i
$598$		0			0
$599$			11.5870i			0.473430i	0.971579	+	0.236715i	$0.0760708\pi$
$599$			11.5870i			0.473430i	−0.971579	+	0.236715i	$0.923929\pi$
$600$	−8.02213	+	19.2806i	−0.327502	+	0.787128i
$601$	2.26709	−	3.92671i	0.0924764	−	0.160174i	−0.816076	−	0.577944i	$-0.803855\pi$
$601$	2.26709	−	3.92671i	0.0924764	−	0.160174i	0.908553	+	0.417771i	$0.137188\pi$
$602$	22.3477	+	38.7074i	0.910826	+	1.57760i
$603$	11.3820	−	19.5706i	0.463510	−	0.796977i
$604$	−0.866700	+	3.23457i	−0.0352655	+	0.131613i
$605$	3.03509	−	11.3271i	0.123394	−	0.460513i
$606$	27.9481	−	3.63437i	1.13531	−	0.147636i
$607$	−6.51641	−	11.2868i	−0.264493	−	0.458115i	0.702938	−	0.711251i	$-0.251871\pi$
$607$	−6.51641	−	11.2868i	−0.264493	−	0.458115i	−0.967431	+	0.253136i	$0.918538\pi$
$608$	−4.11611	+	7.12932i	−0.166930	+	0.289132i
$609$	17.4342	+	7.25389i	0.706470	+	0.293942i
$610$			10.6583i			0.431544i
$611$		0			0
$612$	−0.159348	+	0.0421562i	−0.00644128	+	0.00170406i
$613$	−3.47446	+	0.930978i	−0.140332	+	0.0376019i	−0.328301	−	0.944573i	$-0.606476\pi$
$613$	−3.47446	+	0.930978i	−0.140332	+	0.0376019i	0.187969	+	0.982175i	$0.439809\pi$
$614$	22.4414	+	12.9565i	0.905661	+	0.522884i
$615$	−19.6605	−	2.62007i	−0.792789	−	0.105652i
$616$	−16.4447	−	16.4447i	−0.662575	−	0.662575i
$617$	6.41496	+	1.71888i	0.258257	+	0.0691997i	0.385624	−	0.922656i	$-0.373986\pi$
$617$	6.41496	+	1.71888i	0.258257	+	0.0691997i	−0.127368	+	0.991856i	$0.540653\pi$
$618$	−10.2740	+	7.85767i	−0.413281	+	0.316082i
$619$	13.3334	−	13.3334i	0.535916	−	0.535916i	−0.386411	−	0.922327i	$-0.626285\pi$
$619$	13.3334	−	13.3334i	0.535916	−	0.535916i	0.922327	+	0.386411i	$0.126285\pi$
$620$	0.560039	−	0.323339i	0.0224917	−	0.0129856i
$621$	−10.3762	−	13.6565i	−0.416383	−	0.548018i
$622$	9.16628	+	34.2090i	0.367534	+	1.37166i
$623$	−3.20885			−0.128560
$624$		0			0
$625$	28.8959			1.15584
$626$	8.14365	+	30.3925i	0.325486	+	1.21473i
$627$	−9.33488	−	22.6378i	−0.372799	−	0.904069i
$628$	−0.781896	+	0.451428i	−0.0312011	+	0.0180139i
$629$	0.717411	−	0.717411i	0.0286051	−	0.0286051i
$630$	34.5770	+	0.109636i	1.37758	+	0.00436800i
$631$	−1.42316	−	0.381334i	−0.0566550	−	0.0151807i	0.230380	−	0.973101i	$-0.426003\pi$
$631$	−1.42316	−	0.381334i	−0.0566550	−	0.0151807i	−0.287035	+	0.957920i	$0.592670\pi$
$632$	23.5364	+	23.5364i	0.936227	+	0.936227i
$633$	0.183561	−	1.37740i	0.00729588	−	0.0547469i
$634$	34.8763	+	20.1358i	1.38511	+	0.799696i
$635$	−27.9450	+	7.48784i	−1.10896	+	0.297146i
$636$	5.16828	+	3.97879i	0.204936	+	0.157769i
$637$		0			0
$638$		−	13.0566i		−	0.516915i
$639$	−13.9188	+	7.97727i	−0.550618	+	0.315576i
$640$	−12.6581	+	21.9245i	−0.500357	+	0.866644i
$641$	7.43034	+	12.8697i	0.293481	+	0.508323i	0.974630	−	0.223821i	$-0.0718530\pi$
$641$	7.43034	+	12.8697i	0.293481	+	0.508323i	−0.681150	+	0.732144i	$0.738520\pi$
$642$	2.27808	+	17.5183i	0.0899086	+	0.691392i
$643$	12.5754	−	46.9319i	0.495924	−	1.85081i	−0.0288681	−	0.999583i	$-0.509190\pi$
$643$	12.5754	−	46.9319i	0.495924	−	1.85081i	0.524792	−	0.851230i	$-0.324143\pi$
$644$	0.689499	−	2.57325i	0.0271701	−	0.101400i
$645$	−7.82503	−	60.1740i	−0.308110	−	2.36935i
$646$	0.692588	+	1.19960i	0.0272495	+	0.0471975i
$647$	18.8371	−	32.6268i	0.740562	−	1.28269i	−0.211678	−	0.977340i	$-0.567893\pi$
$647$	18.8371	−	32.6268i	0.740562	−	1.28269i	0.952240	−	0.305351i	$-0.0987739\pi$
$648$	−19.1393	+	18.8981i	−0.751864	+	0.742388i
$649$		−	8.89499i		−	0.349159i
$650$		0			0
$651$	−3.12107	−	2.40275i	−0.122324	−	0.0941714i
$652$	−1.55566	+	0.416839i	−0.0609245	+	0.0163247i
$653$	19.2876	+	11.1357i	0.754782	+	0.435774i	0.827419	−	0.561585i	$-0.189808\pi$
$653$	19.2876	+	11.1357i	0.754782	+	0.435774i	−0.0726369	+	0.997358i	$0.523141\pi$
$654$	3.05167	−	22.8992i	0.119330	−	0.895428i
$655$	25.2945	+	25.2945i	0.988339	+	0.988339i
$656$	−12.4054	−	3.32401i	−0.484348	−	0.129781i
$657$	−0.0465742	+	14.6886i	−0.00181703	+	0.573056i
$658$	−16.4729	+	16.4729i	−0.642182	+	0.642182i
$659$	23.2104	−	13.4005i	0.904148	−	0.522010i	0.0256043	−	0.999672i	$-0.491849\pi$
$659$	23.2104	−	13.4005i	0.904148	−	0.522010i	0.878544	+	0.477662i	$0.158516\pi$
$660$	1.46115	+	3.54340i	0.0568751	+	0.137927i
$661$	−4.52232	−	16.8775i	−0.175898	−	0.656459i	−0.996397	−	0.0848116i	$-0.972971\pi$
$661$	−4.52232	−	16.8775i	−0.175898	−	0.656459i	0.820499	−	0.571647i	$-0.193696\pi$
$662$	0.871200			0.0338602
$663$		0			0
$664$	−7.77728			−0.301817
$665$	12.0567	+	44.9962i	0.467538	+	1.74488i
$666$	5.26317	−	19.3962i	0.203944	−	0.751587i
$667$	10.6700	−	6.16031i	0.413143	−	0.238528i
$668$	0.308966	−	0.308966i	0.0119543	−	0.0119543i
$669$	4.25131	−	3.25145i	0.164365	−	0.125708i
$670$	28.7653	+	7.70763i	1.11130	+	0.297772i
$671$	5.08844	+	5.08844i	0.196437	+	0.196437i
$672$	−7.77963	−	1.03676i	−0.300106	−	0.0399938i
$673$	30.8369	+	17.8037i	1.18867	+	0.686281i	0.958005	−	0.286751i	$-0.0925753\pi$
$673$	30.8369	+	17.8037i	1.18867	+	0.686281i	0.230669	+	0.973032i	$0.425909\pi$
$674$	−31.8144	+	8.52464i	−1.22544	+	0.328357i
$675$	−19.3288	−	8.11416i	−0.743965	−	0.312314i
$676$		0			0
$677$		−	16.3795i		−	0.629517i	−0.949172	−	0.314758i	$-0.898076\pi$
$677$		−	16.3795i		−	0.629517i	0.949172	−	0.314758i	$-0.101924\pi$
$678$	−35.8760	−	14.9270i	−1.37781	−	0.573267i
$679$	−17.7641	+	30.7683i	−0.681723	+	1.18078i
$680$	−0.893032	−	1.54678i	−0.0342462	−	0.0593162i
$681$	−44.5104	+	5.78813i	−1.70564	+	0.221801i
$682$	−0.704886	+	2.63067i	−0.0269915	+	0.100734i
$683$	−9.94232	+	37.1052i	−0.380432	+	1.41979i	0.464811	+	0.885410i	$0.346122\pi$
$683$	−9.94232	+	37.1052i	−0.380432	+	1.41979i	−0.845243	+	0.534382i	$0.820544\pi$
$684$	−3.80253	−	2.21150i	−0.145394	−	0.0845588i
$685$	−26.1431	−	45.2812i	−0.998876	−	1.73010i
$686$	−10.4862	+	18.1626i	−0.400364	+	0.693451i
$687$	18.4815	−	44.4190i	0.705114	−	1.69469i
$688$		−	39.2915i		−	1.49797i
$689$		0			0
$690$	13.7624	−	17.8767i	0.523924	−	0.680554i
$691$	18.6598	−	4.99988i	0.709853	−	0.190204i	0.114213	−	0.993456i	$-0.463565\pi$
$691$	18.6598	−	4.99988i	0.709853	−	0.190204i	0.595640	+	0.803252i	$0.296899\pi$
$692$	2.97299	+	1.71645i	0.113016	+	0.0652498i
$693$	16.5599	−	16.4552i	0.629058	−	0.625081i
$694$	15.2344	+	15.2344i	0.578292	+	0.578292i
$695$	6.76192	+	1.81185i	0.256494	+	0.0687274i
$696$	−11.7379	−	15.3474i	−0.444923	−	0.581742i
$697$	0.535651	−	0.535651i	0.0202892	−	0.0202892i
$698$	−34.0809	+	19.6766i	−1.28998	+	0.744771i
$699$	−23.1464	+	9.54457i	−0.875476	+	0.361009i
$700$	−0.842728	−	3.14510i	−0.0318521	−	0.118874i
$701$	−12.7471			−0.481453			−0.240726	−	0.970593i	$-0.577386\pi$
$701$	−12.7471			−0.481453			−0.240726	+	0.970593i	$0.577386\pi$
$702$		0			0
$703$	27.0761			1.02120
$704$	6.05362	+	22.5924i	0.228154	+	0.851483i
$705$	29.2397	−	12.0572i	1.10123	−	0.454101i
$706$	7.66111	−	4.42315i	0.288330	−	0.166467i
$707$	−25.5967	+	25.5967i	−0.962664	+	0.962664i
$708$	−0.970732	−	1.26924i	−0.0364823	−	0.0477011i
$709$	42.1029	+	11.2814i	1.58121	+	0.423683i	0.939299	−	0.343099i	$-0.111477\pi$
$709$	42.1029	+	11.2814i	1.58121	+	0.423683i	0.641907	+	0.766782i	$0.278143\pi$
$710$	−14.9216	−	14.9216i	−0.559999	−	0.559999i
$711$	−23.7013	+	23.5514i	−0.888866	+	0.883247i
$712$	2.84346	+	1.64168i	0.106563	+	0.0615244i
$713$	−2.48239	+	0.665155i	−0.0929663	+	0.0249102i
$714$	−0.805586	+	1.04642i	−0.0301483	+	0.0391613i
$715$		0			0
$716$		−	4.50497i		−	0.168359i
$717$	3.99203	−	9.59455i	0.149085	−	0.358315i
$718$	6.28386	−	10.8840i	0.234512	−	0.406186i
$719$	17.7809	+	30.7974i	0.663116	+	1.14855i	0.979793	+	0.200017i	$0.0640996\pi$
$719$	17.7809	+	30.7974i	0.663116	+	1.14855i	−0.316677	+	0.948534i	$0.602567\pi$
$720$	−26.2759	−	15.2817i	−0.979245	−	0.569515i
$721$	4.29980	−	16.0471i	0.160133	−	0.597624i
$722$	−3.11143	+	11.6120i	−0.115795	+	0.432154i
$723$	−42.3873	+	5.51205i	−1.57640	+	0.204995i
$724$	−1.28441	−	2.22467i	−0.0477348	−	0.0826791i
$725$	7.52933	−	13.0412i	0.279632	−	0.484338i
$726$	8.19116	+	3.40812i	0.304003	+	0.126487i
$727$			26.2936i			0.975176i	0.873074	+	0.487588i	$0.162123\pi$
$727$			26.2936i			0.975176i	−0.873074	+	0.487588i	$0.837877\pi$
$728$		0			0
$729$	−18.9094	−	19.2726i	−0.700349	−	0.713801i
$730$	−18.6629	+	5.00071i	−0.690745	+	0.185084i
$731$	2.00706	+	1.15878i	0.0742338	+	0.0428589i
$732$	1.28139	+	0.170766i	0.0473617	+	0.00631168i
$733$	−5.72217	−	5.72217i	−0.211353	−	0.211353i	0.593489	−	0.804842i	$-0.297750\pi$
$733$	−5.72217	−	5.72217i	−0.211353	−	0.211353i	−0.804842	+	0.593489i	$0.797750\pi$
$734$	−15.2517	−	4.08668i	−0.562951	−	0.150842i
$735$	−6.33012	+	4.84134i	−0.233490	+	0.178576i
$736$	−3.62099	+	3.62099i	−0.133471	+	0.133471i
$737$	17.4127	−	10.0532i	0.641403	−	0.370314i
$738$	3.92971	−	14.4821i	0.144655	−	0.533092i
$739$	−5.31693	−	19.8431i	−0.195587	−	0.729939i	−0.992114	−	0.125337i	$-0.959999\pi$
$739$	−5.31693	−	19.8431i	−0.195587	−	0.729939i	0.796528	−	0.604602i	$-0.206668\pi$
$740$	−4.23811			−0.155796
$741$		0			0
$742$	52.2565			1.91840
$743$	−8.90116	−	33.2196i	−0.326552	−	1.21871i	−0.912743	−	0.408535i	$-0.866040\pi$
$743$	−8.90116	−	33.2196i	−0.326552	−	1.21871i	0.586191	−	0.810173i	$-0.300627\pi$
$744$	1.53641	+	3.72593i	0.0563277	+	0.136599i
$745$	−41.0648	+	23.7087i	−1.50450	+	0.868621i
$746$	−12.4015	+	12.4015i	−0.454051	+	0.454051i
$747$	0.0247543	−	7.80701i	0.000905711	−	0.285643i
$748$	−0.141398	−	0.0378875i	−0.00517003	−	0.00138531i
$749$	−16.0445	−	16.0445i	−0.586252	−	0.586252i
$750$	−0.871910	+	6.54264i	−0.0318377	+	0.238904i
$751$	25.8847	+	14.9445i	0.944546	+	0.545334i	0.891382	−	0.453252i	$-0.149736\pi$
$751$	25.8847	+	14.9445i	0.944546	+	0.545334i	0.0531635	+	0.998586i	$0.483070\pi$
$752$	19.7818	−	5.30051i	0.721367	−	0.193290i
$753$	−29.8233	−	22.9594i	−1.08682	−	0.836687i
$754$		0			0
$755$		−	36.4243i		−	1.32562i
$756$	0.567166	−	4.15524i	0.0206276	−	0.151125i
$757$	−11.1534	+	19.3182i	−0.405376	+	0.702132i	−0.994365	−	0.106009i	$-0.966193\pi$
$757$	−11.1534	+	19.3182i	−0.405376	+	0.702132i	0.588989	+	0.808141i	$0.299526\pi$
$758$	−20.3284	−	35.2098i	−0.738360	−	1.27888i
$759$	−1.96424	−	15.1049i	−0.0712975	−	0.548274i
$760$	12.3366	−	46.0409i	0.447496	−	1.67008i
$761$	6.85369	−	25.5783i	0.248446	−	0.927214i	−0.723174	−	0.690666i	$-0.757317\pi$
$761$	6.85369	−	25.5783i	0.248446	−	0.927214i	0.971620	−	0.236547i	$-0.0760159\pi$
$762$	−2.82251	−	21.7050i	−0.102249	−	0.786288i
$763$	14.8361	+	25.6968i	0.537101	+	0.930287i
$764$	0.280241	−	0.485391i	0.0101387	−	0.0175608i
$765$	1.55553	−	0.891522i	0.0562403	−	0.0322330i
$766$		−	13.4621i		−	0.486404i
$767$		0			0
$768$	8.92027	+	6.86726i	0.321882	+	0.247801i
$769$	−11.8606	+	3.17804i	−0.427704	+	0.114603i	−0.466248	−	0.884654i	$-0.654395\pi$
$769$	−11.8606	+	3.17804i	−0.427704	+	0.114603i	0.0385441	+	0.999257i	$0.487728\pi$
$770$	26.5940	+	15.3540i	0.958380	+	0.553321i
$771$	−3.73200	+	28.0042i	−0.134405	+	1.00855i
$772$	0.776254	+	0.776254i	0.0279380	+	0.0279380i
$773$	−22.2683	−	5.96678i	−0.800937	−	0.214610i	−0.164941	−	0.986303i	$-0.552744\pi$
$773$	−22.2683	−	5.96678i	−0.800937	−	0.214610i	−0.635995	+	0.771693i	$0.719410\pi$
$774$	45.9080	+	0.145564i	1.65013	+	0.00523219i
$775$	−2.22108	+	2.22108i	−0.0797837	+	0.0797837i
$776$	31.4827	−	18.1765i	1.13016	−	0.652500i
$777$	9.84066	+	23.8644i	0.353032	+	0.856131i
$778$	−10.2305	−	38.1807i	−0.366780	−	1.36884i
$779$	20.2162			0.724321
$780$		0			0
$781$	−14.2476			−0.509818
$782$	0.223010	+	0.832286i	0.00797484	+	0.0297625i
$783$	15.4434	−	11.7339i	0.551903	−	0.419335i
$784$	−4.46886	+	2.58010i	−0.159602	+	0.0921463i
$785$	6.94420	−	6.94420i	0.247849	−	0.247849i
$786$	−21.4969	+	16.4411i	−0.766769	+	0.586434i
$787$	47.8331	+	12.8168i	1.70507	+	0.456871i	0.974207	−	0.225657i	$-0.0724529\pi$
$787$	47.8331	+	12.8168i	1.70507	+	0.456871i	0.730859	+	0.682528i	$0.239120\pi$
$788$	1.34625	+	1.34625i	0.0479581	+	0.0479581i
$789$	19.7375	+	2.63034i	0.702675	+	0.0936425i
$790$	−38.0625	−	21.9754i	−1.35420	−	0.781849i
$791$	48.2086	−	12.9174i	1.71410	−	0.459292i
$792$	−23.0929	+	6.10931i	−0.820570	+	0.217085i
$793$		0			0
$794$		−	4.50589i		−	0.159908i
$795$	−65.5023	−	27.2537i	−2.32313	−	0.966588i
$796$	−0.876045	+	1.51735i	−0.0310506	+	0.0537812i
$797$	2.55365	+	4.42306i	0.0904550	+	0.156673i	0.907703	−	0.419614i	$-0.137835\pi$
$797$	2.55365	+	4.42306i	0.0904550	+	0.156673i	−0.817248	+	0.576287i	$0.804501\pi$
$798$	−34.9487	+	4.54473i	−1.23717	+	0.160882i
$799$	−0.312643	+	1.16680i	−0.0110605	+	0.0412784i
$800$	−1.61991	+	6.04560i	−0.0572726	+	0.213744i
$801$	−1.65700	+	2.84911i	−0.0585472	+	0.100668i
$802$	−13.0976	−	22.6856i	−0.462491	−	0.801058i
$803$	−6.52251	+	11.2973i	−0.230175	+	0.398674i
$804$	1.38752	−	3.33480i	0.0489339	−	0.117609i
$805$			28.9772i			1.02131i
$806$		0			0
$807$	−11.7692	+	15.2877i	−0.414295	+	0.538151i
$808$	35.7776	−	9.58659i	1.25865	−	0.337255i
$809$	−0.216848	−	0.125197i	−0.00762398	−	0.00440171i	0.496183	−	0.868218i	$-0.334734\pi$
$809$	−0.216848	−	0.125197i	−0.00762398	−	0.00440171i	−0.503807	+	0.863816i	$0.668068\pi$
$810$	17.9524	−	30.6440i	0.630783	−	1.07672i
$811$	−0.345058	−	0.345058i	−0.0121166	−	0.0121166i	0.701023	−	0.713139i	$-0.252727\pi$
$811$	−0.345058	−	0.345058i	−0.0121166	−	0.0121166i	−0.713139	+	0.701023i	$0.752727\pi$
$812$	2.90994	+	0.779717i	0.102119	+	0.0273627i
$813$	6.39404	+	8.36028i	0.224249	+	0.293208i
$814$	12.6210	−	12.6210i	0.442364	−	0.442364i
$815$	15.1712	−	8.75912i	0.531425	−	0.306818i
$816$	1.07326	−	0.442566i	0.0375715	−	0.0154929i
$817$	16.0077	+	59.7416i	0.560039	+	2.09009i
$818$	7.27498			0.254364
$819$		0			0
$820$	−3.16436			−0.110504
$821$	7.44280	+	27.7769i	0.259756	+	0.969421i	0.965383	+	0.260838i	$0.0839987\pi$
$821$	7.44280	+	27.7769i	0.259756	+	0.969421i	−0.705627	+	0.708583i	$0.749335\pi$
$822$	36.5702	−	15.0800i	1.27553	−	0.525975i
$823$	−1.74844	+	1.00946i	−0.0609468	+	0.0351877i	−0.530164	−	0.847895i	$-0.677870\pi$
$823$	−1.74844	+	1.00946i	−0.0609468	+	0.0351877i	0.469217	+	0.883083i	$0.344536\pi$
$824$	−12.0200	+	12.0200i	−0.418737	+	0.418737i
$825$	−11.3100	−	14.7879i	−0.393763	−	0.514850i
$826$	−12.3659	−	3.31344i	−0.430265	−	0.115289i
$827$	−0.657151	−	0.657151i	−0.0228514	−	0.0228514i	0.695589	−	0.718440i	$-0.255144\pi$
$827$	−0.657151	−	0.657151i	−0.0228514	−	0.0228514i	−0.718440	+	0.695589i	$0.755144\pi$
$828$	−1.92872	−	1.94099i	−0.0670275	−	0.0674539i
$829$	40.2809	+	23.2562i	1.39902	+	0.807722i	0.994289	−	0.106716i	$-0.0340337\pi$
$829$	40.2809	+	23.2562i	1.39902	+	0.807722i	0.404726	+	0.914438i	$0.367367\pi$
$830$	9.91936	−	2.65788i	0.344306	−	0.0922565i
$831$	29.3530	−	38.1282i	1.01824	−	1.32265i
$832$		0			0
$833$		−	0.304367i		−	0.0105457i
$834$	−2.03453	+	4.88986i	−0.0704501	+	0.169322i
$835$	−2.37637	+	4.11600i	−0.0822377	+	0.142440i
$836$	−1.95332	−	3.38325i	−0.0675570	−	0.117012i
$837$	−3.74506	+	1.53043i	−0.129448	+	0.0528993i
$838$	11.7007	−	43.6675i	0.404193	−	1.50847i
$839$	11.2534	−	41.9982i	0.388510	−	1.44994i	−0.444048	−	0.896003i	$-0.646458\pi$
$839$	11.2534	−	41.9982i	0.388510	−	1.44994i	0.832558	−	0.553937i	$-0.186875\pi$
$840$	45.0633	−	5.86003i	1.55483	−	0.202190i
$841$	−7.53364	−	13.0486i	−0.259781	−	0.449953i
$842$	17.2806	−	29.9309i	0.595530	−	1.03149i
$843$	−26.2762	−	10.9328i	−0.905000	−	0.376545i
$844$		−	0.221693i		−	0.00763098i
$845$		0			0
$846$	6.11981	+	23.1326i	0.210403	+	0.795314i
$847$	−11.0069	+	2.94930i	−0.378203	+	0.101339i
$848$	−39.7838	−	22.9692i	−1.36618	−	0.788765i
$849$	45.6466	+	6.08313i	1.56659	+	0.208773i
$850$	0.744677	+	0.744677i	0.0255422	+	0.0255422i
$851$	16.2688	+	4.35920i	0.557686	+	0.149431i
$852$	−2.03301	+	1.55487i	−0.0696499	+	0.0532690i
$853$	−0.0191114	+	0.0191114i	−0.000654362	+	0.000654362i	−0.707434	−	0.706780i	$-0.750147\pi$
$853$	−0.0191114	+	0.0191114i	−0.000654362	+	0.000654362i	0.706780	+	0.707434i	$0.250147\pi$
$854$	8.96948	−	5.17853i	0.306929	−	0.177206i
$855$	46.1776	+	12.5303i	1.57924	+	0.428528i
$856$	6.00903	+	22.4260i	0.205384	+	0.766505i
$857$	5.89068			0.201222			0.100611	−	0.994926i	$-0.467920\pi$
$857$	5.89068			0.201222			0.100611	+	0.994926i	$0.467920\pi$
$858$		0			0
$859$	11.6341			0.396949			0.198475	−	0.980106i	$-0.436401\pi$
$859$	11.6341			0.396949			0.198475	+	0.980106i	$0.436401\pi$
$860$	−2.50562	−	9.35109i	−0.0854408	−	0.318870i
$861$	7.34747	+	17.8182i	0.250401	+	0.607243i
$862$	−12.8577	+	7.42341i	−0.437936	+	0.252842i
$863$	−19.9075	+	19.9075i	−0.677660	+	0.677660i	−0.959470	−	0.281811i	$-0.909065\pi$
$863$	−19.9075	+	19.9075i	−0.677660	+	0.677660i	0.281811	+	0.959470i	$0.409065\pi$
$864$	−4.93781	+	6.37210i	−0.167988	+	0.216783i
$865$	−36.0682	−	9.66445i	−1.22636	−	0.328601i
$866$	−5.76148	−	5.76148i	−0.195783	−	0.195783i
$867$	3.88056	−	29.1190i	0.131791	−	0.988932i
$868$	−0.544208	−	0.314199i	−0.0184716	−	0.0106646i
$869$	−28.6629	+	7.68020i	−0.972323	+	0.260533i
$870$	20.2158	+	15.5631i	0.685379	+	0.527638i
$871$		0			0
$872$		−	30.3610i		−	1.02815i
$873$	18.1458	+	31.6609i	0.614142	+	1.07156i
$874$	−11.4975	+	19.9142i	−0.388908	+	0.673608i
$875$	−4.23889	−	7.34198i	−0.143301	−	0.248204i
$876$	0.302194	+	2.32385i	0.0102102	+	0.0785158i
$877$	−3.60580	+	13.4570i	−0.121759	+	0.454412i	−0.999703	−	0.0243510i	$-0.992248\pi$
$877$	−3.60580	+	13.4570i	−0.121759	+	0.454412i	0.877944	+	0.478763i	$0.158915\pi$
$878$	−13.1784	+	49.1824i	−0.444749	+	1.65983i
$879$	0.646595	+	4.97228i	0.0218091	+	0.167711i
$880$	−13.4976	−	23.3786i	−0.455005	−	0.788092i
$881$	−3.83326	+	6.63940i	−0.129146	+	0.223687i	−0.923346	−	0.383969i	$-0.874557\pi$
$881$	−3.83326	+	6.63940i	−0.129146	+	0.223687i	0.794200	+	0.607656i	$0.207890\pi$
$882$	−2.99802	−	5.23095i	−0.100948	−	0.176135i
$883$			7.52156i			0.253121i	0.991959	+	0.126560i	$0.0403937\pi$
$883$			7.52156i			0.253121i	−0.991959	+	0.126560i	$0.959606\pi$
$884$		0			0
$885$	13.7723	+	10.6026i	0.462951	+	0.356403i
$886$	23.2239	−	6.22283i	0.780222	−	0.209060i
$887$	−36.5051	−	21.0762i	−1.22572	−	0.707670i	−0.259589	−	0.965719i	$-0.583587\pi$
$887$	−36.5051	−	21.0762i	−1.22572	−	0.707670i	−0.966132	+	0.258049i	$0.916920\pi$
$888$	3.48911	−	26.1816i	0.117087	−	0.878597i
$889$	19.8789	+	19.8789i	0.666716	+	0.666716i
$890$	−4.18768	−	1.12208i	−0.140371	−	0.0376123i
$891$	−6.05915	−	23.2006i	−0.202989	−	0.777249i
$892$	0.603784	−	0.603784i	0.0202162	−	0.0202162i
$893$	−27.9181	+	16.1185i	−0.934245	+	0.539386i
$894$	−13.6758	−	33.1649i	−0.457387	−	1.10920i
$895$	12.6826	+	47.3319i	0.423931	+	1.58213i
$896$	24.6007			0.821850
$897$		0			0
$898$	−2.54586			−0.0849564
$899$	−0.752187	−	2.80720i	−0.0250868	−	0.0936254i
$900$	−3.22768	−	0.875834i	−0.107589	−	0.0291945i
$901$	2.34659	−	1.35480i	0.0781762	−	0.0451351i
$902$	9.42336	−	9.42336i	0.313764	−	0.313764i
$903$	−46.8372	+	35.8216i	−1.55865	+	1.19207i
$904$	−49.3279	−	13.2174i	−1.64062	−	0.439603i
$905$	19.7578	+	19.7578i	0.656771	+	0.656771i
$906$	27.3155	+	3.64021i	0.907496	+	0.120938i
$907$	−32.3487	−	18.6765i	−1.07412	−	0.620143i	−0.144815	−	0.989459i	$-0.546259\pi$
$907$	−32.3487	−	18.6765i	−1.07412	−	0.620143i	−0.929304	+	0.369316i	$0.879592\pi$
$908$	−6.91694	+	1.85339i	−0.229547	+	0.0615069i
$909$	9.50935	+	35.9449i	0.315405	+	1.19222i
$910$		0			0
$911$		−	20.5977i		−	0.682434i	−0.939985	−	0.341217i	$-0.889161\pi$
$911$		−	20.5977i		−	0.682434i	0.939985	−	0.341217i	$-0.110839\pi$
$912$	28.6047	+	11.9016i	0.947195	+	0.394102i
$913$	3.46673	−	6.00455i	0.114732	−	0.198722i
$914$	3.82525	+	6.62553i	0.126528	+	0.219153i
$915$	−13.9438	+	1.81326i	−0.460969	+	0.0599444i
$916$	1.98657	−	7.41398i	0.0656381	−	0.244965i
$917$	8.99672	−	33.5762i	0.297098	−	1.10878i
$918$	0.513116	+	1.25563i	0.0169353	+	0.0414419i
$919$	19.6678	+	34.0657i	0.648782	+	1.12372i	0.983414	+	0.181375i	$0.0580546\pi$
$919$	19.6678	+	34.0657i	0.648782	+	1.12372i	−0.334632	+	0.942349i	$0.608612\pi$
$920$	14.8250	−	25.6776i	0.488765	−	0.846567i
$921$	−13.1326	+	31.5633i	−0.432734	+	1.04005i
$922$		−	18.7869i		−	0.618715i
$923$		0			0
$924$	2.27201	−	2.95124i	0.0747437	−	0.0970888i
$925$	19.8842	−	5.32796i	0.653789	−	0.175182i
$926$	4.80838	+	2.77612i	0.158013	+	0.0912289i
$927$	−12.0277	−	12.1042i	−0.395041	−	0.397555i
$928$	−4.09478	−	4.09478i	−0.134418	−	0.134418i
$929$	−20.3200	−	5.44472i	−0.666676	−	0.178635i	−0.0904192	−	0.995904i	$-0.528821\pi$
$929$	−20.3200	−	5.44472i	−0.666676	−	0.178635i	−0.576257	+	0.817268i	$0.695487\pi$
$930$	−3.23292	−	4.22708i	−0.106012	−	0.138611i
$931$	5.74361	−	5.74361i	0.188239	−	0.188239i
$932$	−3.45925	+	1.99720i	−0.113311	+	0.0654204i
$933$	−43.1947	+	17.8117i	−1.41413	+	0.583127i
$934$	−12.7460	−	47.5689i	−0.417063	−	1.55650i
$935$	1.59228			0.0520730
$936$		0			0
$937$	2.05438			0.0671138			0.0335569	−	0.999437i	$-0.489317\pi$
$937$	2.05438			0.0671138			0.0335569	+	0.999437i	$0.489317\pi$
$938$	−7.48976	−	27.9521i	−0.244549	−	0.912670i
$939$	−38.3757	+	15.8245i	−1.25234	+	0.516413i
$940$	4.36990	−	2.52297i	0.142531	−	0.0822901i
$941$	41.3493	−	41.3493i	1.34795	−	1.34795i	0.460059	−	0.887888i	$-0.347828\pi$
$941$	41.3493	−	41.3493i	1.34795	−	1.34795i	0.887888	−	0.460059i	$-0.152172\pi$
$942$	4.51363	+	5.90163i	0.147062	+	0.192285i
$943$	12.1470	+	3.25477i	0.395560	+	0.105990i
$944$	7.95798	+	7.95798i	0.259010	+	0.259010i
$945$	5.73900	+	45.2542i	0.186690	+	1.47212i
$946$	35.3089	+	20.3856i	1.14799	+	0.662793i
$947$	29.2370	−	7.83402i	0.950074	−	0.254571i	0.249680	−	0.968328i	$-0.419675\pi$
$947$	29.2370	−	7.83402i	0.950074	−	0.254571i	0.700393	+	0.713757i	$0.253008\pi$
$948$	−3.25181	+	4.22395i	−0.105614	+	0.137188i
$949$		0			0
$950$			28.1052i			0.911852i
$951$	−20.4094	+	49.0527i	−0.661822	+	1.59064i
$952$	−0.867788	+	1.50305i	−0.0281252	+	0.0487142i
$953$	4.74184	+	8.21310i	0.153603	+	0.266048i	0.932550	−	0.361042i	$-0.117579\pi$
$953$	4.74184	+	8.21310i	0.153603	+	0.266048i	−0.778946	+	0.627091i	$0.784246\pi$
$954$	26.9845	−	46.3981i	0.873654	−	1.50219i
$955$	−1.57789	+	5.88875i	−0.0510592	+	0.190556i
$956$	0.429101	−	1.60143i	0.0138781	−	0.0517938i
$957$	17.0813	−	2.22125i	0.552161	−	0.0718030i
$958$	−1.34066	−	2.32209i	−0.0433147	−	0.0750233i
$959$	−25.4041	+	44.0012i	−0.820341	+	1.42087i
$960$	−42.1961	−	17.5566i	−1.36187	−	0.566637i
$961$		−	30.3938i		−	0.980445i
$962$		0			0
$963$	−22.5308	+	5.96062i	−0.726046	+	0.192078i
$964$	−6.58703	+	1.76499i	−0.212154	+	0.0568465i
$965$	−10.3411	−	5.97046i	−0.332893	−	0.192196i
$966$	−21.7307	−	2.89596i	−0.699174	−	0.0931759i
$967$	−17.7922	−	17.7922i	−0.572158	−	0.572158i	0.360573	−	0.932731i	$-0.382581\pi$
$967$	−17.7922	−	17.7922i	−0.572158	−	0.572158i	−0.932731	+	0.360573i	$0.882581\pi$
$968$	11.2625	+	3.01778i	0.361990	+	0.0969950i
$969$	−1.45155	+	1.11016i	−0.0466306	+	0.0356636i
$970$	−33.9421	+	33.9421i	−1.08981	+	1.08981i
$971$	−16.0499	+	9.26639i	−0.515065	+	0.297373i	−0.734913	−	0.678161i	$-0.762777\pi$
$971$	−16.0499	+	9.26639i	−0.515065	+	0.297373i	0.219848	+	0.975534i	$0.429444\pi$
$972$	−3.39653	−	2.64929i	−0.108944	−	0.0849759i
$973$	−1.76063	−	6.57078i	−0.0564434	−	0.210649i
$974$	−32.9285			−1.05510
$975$		0			0
$976$	−9.10483			−0.291439
$977$	−7.96925	−	29.7416i	−0.254959	−	0.951519i	−0.968113	−	0.250512i	$-0.919401\pi$
$977$	−7.96925	−	29.7416i	−0.254959	−	0.951519i	0.713155	−	0.701007i	$-0.247266\pi$
$978$	5.05248	+	12.2527i	0.161560	+	0.391797i
$979$	−2.53495	+	1.46355i	−0.0810174	+	0.0467754i
$980$	−0.899023	+	0.899023i	−0.0287182	+	0.0287182i
$981$	30.4771	+	0.0966359i	0.973058	+	0.00308535i
$982$	−9.55192	−	2.55943i	−0.304814	−	0.0816747i
$983$	−19.1428	−	19.1428i	−0.610561	−	0.610561i	0.332531	−	0.943092i	$-0.392097\pi$
$983$	−19.1428	−	19.1428i	−0.610561	−	0.610561i	−0.943092	+	0.332531i	$0.892097\pi$
$984$	2.60512	−	19.5483i	0.0830483	−	0.623178i
$985$	−17.9345	−	10.3545i	−0.571441	−	0.329921i
$986$	−0.941188	+	0.252190i	−0.0299735	+	0.00803138i
$987$	−24.3533	−	18.7483i	−0.775173	−	0.596766i
$988$		0			0
$989$			38.4731i			1.22337i
$990$	27.3654	−	15.6840i	0.869731	−	0.498469i
$991$	−3.12167	+	5.40689i	−0.0991631	+	0.171755i	−0.911338	−	0.411658i	$-0.864950\pi$
$991$	−3.12167	+	5.40689i	−0.0991631	+	0.171755i	0.812175	+	0.583413i	$0.198283\pi$
$992$	0.603961	+	1.04609i	0.0191758	+	0.0332134i
$993$	0.148213	+	1.13975i	0.00470341	+	0.0361689i
$994$	−5.30731	+	19.8071i	−0.168338	+	0.628244i
$995$	4.93255	−	18.4085i	0.156372	−	0.583589i
$996$	−0.160617	−	1.23513i	−0.00508933	−	0.0391367i
$997$	0.917609	+	1.58935i	0.0290610	+	0.0503351i	0.880190	−	0.474621i	$-0.157415\pi$
$997$	0.917609	+	1.58935i	0.0290610	+	0.0503351i	−0.851129	+	0.524956i	$0.824082\pi$
$998$	8.09094	−	14.0139i	0.256114	−	0.443603i
$999$	26.2706	+	3.58578i	0.831164	+	0.113449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.488.8		96
3.2	odd	2	inner	507.2.k.k.488.17		96
13.2	odd	12	inner	507.2.k.k.80.17		96
13.3	even	3	inner	507.2.k.k.89.17		96
13.4	even	6		507.2.f.g.437.17	yes	48
13.5	odd	4	inner	507.2.k.k.188.8		96
13.6	odd	12		507.2.f.g.239.17	yes	48
13.7	odd	12		507.2.f.g.239.7	✓	48
13.8	odd	4	inner	507.2.k.k.188.18		96
13.9	even	3		507.2.f.g.437.7	yes	48
13.10	even	6	inner	507.2.k.k.89.7		96
13.11	odd	12	inner	507.2.k.k.80.7		96
13.12	even	2	inner	507.2.k.k.488.18		96
39.2	even	12	inner	507.2.k.k.80.8		96
39.5	even	4	inner	507.2.k.k.188.17		96
39.8	even	4	inner	507.2.k.k.188.7		96
39.11	even	12	inner	507.2.k.k.80.18		96
39.17	odd	6		507.2.f.g.437.8	yes	48
39.20	even	12		507.2.f.g.239.18	yes	48
39.23	odd	6	inner	507.2.k.k.89.18		96
39.29	odd	6	inner	507.2.k.k.89.8		96
39.32	even	12		507.2.f.g.239.8	yes	48
39.35	odd	6		507.2.f.g.437.18	yes	48
39.38	odd	2	inner	507.2.k.k.488.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.7	✓	48	13.7	odd	12
507.2.f.g.239.8	yes	48	39.32	even	12
507.2.f.g.239.17	yes	48	13.6	odd	12
507.2.f.g.239.18	yes	48	39.20	even	12
507.2.f.g.437.7	yes	48	13.9	even	3
507.2.f.g.437.8	yes	48	39.17	odd	6
507.2.f.g.437.17	yes	48	13.4	even	6
507.2.f.g.437.18	yes	48	39.35	odd	6
507.2.k.k.80.7		96	13.11	odd	12	inner
507.2.k.k.80.8		96	39.2	even	12	inner
507.2.k.k.80.17		96	13.2	odd	12	inner
507.2.k.k.80.18		96	39.11	even	12	inner
507.2.k.k.89.7		96	13.10	even	6	inner
507.2.k.k.89.8		96	39.29	odd	6	inner
507.2.k.k.89.17		96	13.3	even	3	inner
507.2.k.k.89.18		96	39.23	odd	6	inner
507.2.k.k.188.7		96	39.8	even	4	inner
507.2.k.k.188.8		96	13.5	odd	4	inner
507.2.k.k.188.17		96	39.5	even	4	inner
507.2.k.k.188.18		96	13.8	odd	4	inner
507.2.k.k.488.7		96	39.38	odd	2	inner
507.2.k.k.488.8		96	1.1	even	1	trivial
507.2.k.k.488.17		96	3.2	odd	2	inner
507.2.k.k.488.18		96	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.339800 - 1.26815i) q^{2} +(1.60126 - 0.660289i) q^{3} +(0.239309 - 0.138165i) q^{4} +(-2.12536 + 2.12536i) q^{5} +(-1.38145 - 1.80627i) q^{6} +(2.82123 + 0.755945i) q^{7} +(-2.11323 - 2.11323i) q^{8} +(2.12804 - 2.11458i) q^{9} +O(q^{10})\)	\(q+(-0.339800 - 1.26815i) q^{2} +(1.60126 - 0.660289i) q^{3} +(0.239309 - 0.138165i) q^{4} +(-2.12536 + 2.12536i) q^{5} +(-1.38145 - 1.80627i) q^{6} +(2.82123 + 0.755945i) q^{7} +(-2.11323 - 2.11323i) q^{8} +(2.12804 - 2.11458i) q^{9} +(3.41747 + 1.97308i) q^{10} +(2.57352 - 0.689573i) q^{11} +(0.291966 - 0.379251i) q^{12} -3.83461i q^{14} +(-1.99989 + 4.80659i) q^{15} +(-1.68549 + 2.91935i) q^{16} +(-0.0994162 - 0.172194i) q^{17} +(-3.40472 - 1.98013i) q^{18} +(1.37337 - 5.12548i) q^{19} +(-0.214967 + 0.802269i) q^{20} +(5.01665 - 0.652364i) q^{21} +(-1.74897 - 3.02930i) q^{22} +(1.65038 - 2.85855i) q^{23} +(-4.77917 - 1.98848i) q^{24} -4.03430i q^{25} +(2.01129 - 4.79111i) q^{27} +(0.779591 - 0.208891i) q^{28} +(3.23258 + 1.86633i) q^{29} +(6.77505 + 0.902881i) q^{30} +(-0.550550 - 0.550550i) q^{31} +(-1.49855 - 0.401535i) q^{32} +(3.66555 - 2.80345i) q^{33} +(-0.184586 + 0.184586i) q^{34} +(-7.60277 + 4.38946i) q^{35} +(0.217097 - 0.800060i) q^{36} +(1.32066 + 4.92878i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(0.986066 + 3.68005i) q^{41} +(-2.53195 - 6.14019i) q^{42} +(-10.0942 + 5.82790i) q^{43} +(0.520592 - 0.520592i) q^{44} +(-0.0285911 + 9.01709i) q^{45} +(-4.18587 - 1.12160i) q^{46} +(-4.29586 - 4.29586i) q^{47} +(-0.771281 + 5.78754i) q^{48} +(1.32568 + 0.765385i) q^{49} +(-5.11610 + 1.37086i) q^{50} +(-0.272889 - 0.210083i) q^{51} +13.6276i q^{53} +(-6.75928 - 0.922602i) q^{54} +(-4.00407 + 6.93525i) q^{55} +(-4.36442 - 7.55939i) q^{56} +(-1.18519 - 9.11402i) q^{57} +(1.26836 - 4.73357i) q^{58} +(0.864088 - 3.22482i) q^{59} +(0.185512 + 1.42658i) q^{60} +(1.35047 + 2.33909i) q^{61} +(-0.511103 + 0.885257i) q^{62} +(7.60218 - 4.35704i) q^{63} +8.77879i q^{64} +(-4.80075 - 3.69585i) q^{66} +(7.28944 - 1.95320i) q^{67} +(-0.0475824 - 0.0274717i) q^{68} +(0.755216 - 5.66699i) q^{69} +(8.14992 + 8.14992i) q^{70} +(-5.16536 - 1.38405i) q^{71} +(-8.96564 - 0.0284280i) q^{72} +(-3.46215 + 3.46215i) q^{73} +(5.80168 - 3.34960i) q^{74} +(-2.66381 - 6.45995i) q^{75} +(-0.379503 - 1.41633i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(-2.62241 - 9.78695i) q^{80} +(0.0570734 - 8.99982i) q^{81} +(4.33179 - 2.50096i) q^{82} +(1.84014 - 1.84014i) q^{83} +(1.11040 - 0.849243i) q^{84} +(0.577269 + 0.154679i) q^{85} +(10.8207 + 10.8207i) q^{86} +(6.40850 + 0.854033i) q^{87} +(-6.89568 - 3.98122i) q^{88} +(-1.06120 + 0.284349i) q^{89} +(11.4447 - 3.02775i) q^{90} -0.912102i q^{92} +(-1.24509 - 0.518049i) q^{93} +(-3.98807 + 6.90753i) q^{94} +(7.97458 + 13.8124i) q^{95} +(-2.66469 + 0.346516i) q^{96} +(-3.14829 + 11.7496i) q^{97} +(0.520155 - 1.94125i) q^{98} +(4.01839 - 6.90936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9}+O(q^{10}) \) 96 * q + 24 * q^9	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

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